- published: 29 May 2019
- views: 175038
-
remove the playlistKernel (linear Algebra)
- remove the playlistKernel (linear Algebra)
Kernel (linear algebra)
In mathematics, and more specifically in linear algebra and functional analysis, the kernel (also known as null space or nullspace) of a linear map L : V → W between two vector spaces V and W, is the set of all elements v of V for which L(v) = 0, where 0 denotes the zero vector in W. That is, in set-builder notation,
Properties of the Kernel
The kernel of L is a linear subspace of the domain V. In the linear map L : V → W, two elements of V have the same image in W if and only if their difference lies in the kernel of L:
It follows that the image of L is isomorphic to the quotient of V by the kernel:
This implies the rank–nullity theorem:
where, by “rank” we mean the dimension of the image of L, and by “nullity” that of the kernel of L.
When V is an inner product space, the quotient V / ker(L) can be identified with the orthogonal complement in V of ker(L). This is the generalization to linear operators of the row space, or coimage, of a matrix.
Application to modules
The notion of kernel applies to the homomorphisms of modules, the latter being a generalization of the vector space over a field to that over a ring. The domain of the mapping is a module, and the kernel constitutes a "submodule". Here, the concepts of rank and nullity do not necessarily apply.
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Kernel_(linear_algebra)
Linear algebra
Linear algebra is the branch of mathematics concerning vector spaces and linear mappings between such spaces. It includes the study of lines, planes, and subspaces, but is also concerned with properties common to all vector spaces.
The set of points with coordinates that satisfy a linear equation forms a hyperplane in an n-dimensional space. The conditions under which a set of n hyperplanes intersect in a single point is an important focus of study in linear algebra. Such an investigation is initially motivated by a system of linear equations containing several unknowns. Such equations are naturally represented using the formalism of matrices and vectors.
Linear algebra is central to both pure and applied mathematics. For instance, abstract algebra arises by relaxing the axioms of a vector space, leading to a number of generalizations. Functional analysis studies the infinite-dimensional version of the theory of vector spaces. Combined with calculus, linear algebra facilitates the solution of linear systems of differential equations.
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Linear_algebra
Kernel (digital media company)
Kernel is a corporation in the United States that sells goods and services relating to feature films, television programs, e-sports, video games, and related content including digital home entertainment, and VIP experiences over the Internet.
E-Commerce
Kernel's e-commerce platform sells movie-related packages that include related content, merchandise, digital home entertainment, and VIP experiences. Kernel was named one of "10 Startups and Technologies to Watch in 2015" by Video Ink.
On October 26, 2015, it was announced that Kernel will begin selling theater tickets to all movies on Kernel.com and its mobile app in the first quarter of 2016 exclusively through its ticketing partner MovieTickets.com on 28,000 screens in 22 countries.
Data Collection
Kernel operates a highly-scalable, transcontinental, massively-distributed, fault-tolerant hadoop cluster to track and analyze big data.
Films
History
In December 2014, Kernel was tapped by Sony Pictures Entertainment to distribute the film The Interview.
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Kernel_(digital_media_company)
Kernel (operating system)
In computing, the kernel is a computer program that manages input/output requests from software, and translates them into data processing instructions for the central processing unit and other electronic components of a computer. The kernel is a fundamental part of a modern computer's operating system.
The critical code of the kernel is usually loaded into a protected area of memory, which prevents it from being overwritten by other, less frequently used parts of the operating system or by applications. The kernel performs its tasks, such as executing processes and handling interrupts, in kernel space, whereas everything a user normally does, such as writing text in a text editor or running programs in a GUI (graphical user interface), is done in user space. This separation prevents user data and kernel data from interfering with each other and thereby diminishing performance or causing the system to become unstable (and possibly crashing).
When a process makes requests of the kernel, the request is called a system call. Various kernel designs differ in how they manage system calls and resources. For example, a monolithic kernel executes all the operating system instructions in the same address space in order to improve the performance of the system. A microkernel runs most of the operating system's background processes in user space, to make the operating system more modular and, therefore, easier to maintain.
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Kernel_(operating_system)
Kernel (algebra)
In the various branches of mathematics that fall under the heading of abstract algebra, the kernel of a homomorphism measures the degree to which the homomorphism fails to be injective. An important special case is the kernel of a linear map. The kernel of a matrix, also called the null space, is the kernel of the linear map defined by the matrix.
The definition of kernel takes various forms in various contexts. But in all of them, the kernel of a homomorphism is trivial (in a sense relevant to that context) if and only if the homomorphism is injective. The fundamental theorem on homomorphisms (or first isomorphism theorem) is a theorem, again taking various forms, that applies to the quotient algebra defined by the kernel.
In this article, we first survey kernels for some important types of algebraic structures; then we give general definitions from universal algebra for generic algebraic structures.
Survey of examples
Linear maps
Let V and W be vector spaces (or more generally modules) and let T be a linear map from V to W. If 0W is the zero vector of W, then the kernel of T is the preimage of the zero subspace {0W}; that is, the subset of V consisting of all those elements of V that are mapped by T to the element 0W. The kernel is usually denoted as ker T, or some variation thereof:
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Kernel_(algebra)
*-algebra
In mathematics, and more specifically in abstract algebra, a *-algebra (or involutive algebra) is a mathematical structure consisting of two involutive rings R and A, where R is commutative and A has the structure of an associative algebra over R. Involutive algebras generalize the idea of a number system equipped with conjugation, for example the complex numbers and complex conjugation, matrices over the complex numbers and conjugate transpose, and linear operators over a Hilbert space and Hermitian adjoints.
Terminology
*-ring
In mathematics, a *-ring is a ring with a map * : A → A that is an antiautomorphism and an involution.
More precisely, * is required to satisfy the following properties:
for all x, y in A.
This is also called an involutive ring, involutory ring, and ring with involution. Note that the third axiom is actually redundant, because the second and fourth axioms imply 1* is also a multiplicative identity, and identities are unique.
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/*-algebra
Algebra
Algebra (from Arabic "al-jabr" meaning "reunion of broken parts") is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics. As such, it includes everything from elementary equation solving to the study of abstractions such as groups, rings, and fields. The more basic parts of algebra are called elementary algebra, the more abstract parts are called abstract algebra or modern algebra. Elementary algebra is generally considered to be essential for any study of mathematics, science, or engineering, as well as such applications as medicine and economics. Abstract algebra is a major area in advanced mathematics, studied primarily by professional mathematicians. Much early work in algebra, as the Arabic origin of its name suggests, was done in the Middle East, by mathematicians such as al-Khwārizmī (780 – 850) and Omar Khayyam (1048–1131).
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Algebra
Podcasts:
-
Image and Kernel
Now that we've learned about linear transformations, we can combine this with what we know about vector spaces to learn about the concepts of image and kernel. Let's get a closer look! Script by Howard Whittle Watch the whole Mathematics playlist: http://bit.ly/ProfDaveMath Classical Physics Tutorials: http://bit.ly/ProfDavePhysics1 Modern Physics Tutorials: http://bit.ly/ProfDavePhysics2 General Chemistry Tutorials: http://bit.ly/ProfDaveGenChem Organic Chemistry Tutorials: http://bit.ly/ProfDaveOrgChem Biochemistry Tutorials: http://bit.ly/ProfDaveBiochem Biology Tutorials: http://bit.ly/ProfDaveBio EMAIL► [email protected] PATREON► http://patreon.com/ProfessorDaveExplains Check out "Is This Wi-Fi Organic?", my book on disarming pseudoscience! Amazon: https://amzn.to/2...
published: 29 May 2019 -
KERNEL and RANGE of a LINEAR TRANSFORMATION - LINEAR ALGEBRA
We discuss the kernal and range of a linear transformation. LIKE AND SHARE THE VIDEO IF IT HELPED! Visit our website: http://bit.ly/1zBPlvm Subscribe on YouTube: http://bit.ly/1vWiRxW Like us on Facebook: http://on.fb.me/1vWwDRc Submit your questions on Reddit: http://bit.ly/1GwZZrP #LinearAlgebra #Algebra #UniversityMath #Lecture *--Playlists--* Linear Algebra: https://www.youtube.com/playlist?list=PLDDGPdw7e6AjJacaEe9awozSaOou-NIx_ *--Recommended Textbooks--* Linear Algebra and Its Applications (Lay): https://amzn.to/37gBZ27 Linear Algebra Done Right (Axler): https://amzn.to/2T0GpBI Introduction to Linear Algebra (Strang): https://amzn.to/3dC6kJq Linear Algebra: Step by Step (Singh): https://amzn.to/2T33G65 3,000 Solved Problems in Linear Algebra (Lipschutz): https://amzn.to/3j2nJMw...
published: 13 May 2016 -
1.6 Ex2 Finding kernel and range
published: 31 Oct 2016 -
Inverse matrices, column space and null space | Chapter 7, Essence of linear algebra
How to think about linear systems of equations geometrically. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Home page: https://www.3blue1brown.com/ Full series: http://3b1b.co/eola Future series like this are funded by the community, through Patreon, where supporters get early access as the series is being produced. http://3b1b.co/support Thanks to these viewers for their contributions to translations Hebrew: Omer Tuchfeld ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are ne...
published: 15 Aug 2016 -
Preimage and kernel example | Matrix transformations | Linear Algebra | Khan Academy
Example involving the preimage of a set under a transformation. Definition of kernel of a transformation. Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/linear_transformations/v/sums-and-scalar-multiples-of-linear-transformations?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra Missed the previous lesson? https://www.khanacademy.org/math/linear-algebra/matrix_transformations/linear_transformations/v/preimage-of-a-set?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into th...
published: 22 Oct 2009 -
Kernel of a matrix - Part 2 | How to determine it! | Linear Algebra | Math2Go
In this video we will look into the kernel of a given matrix / a given linear map. We will learn how to efficiently determine kernels of given matrices. If you want to know more about kernels, see here: https://www.youtube.com/watch?v=fxuI7d32t9o If you have any questions please feel free to ask. You can also ask for specific other mathematical problems in the comment section below! Please comment and subscribe if this video was helpful to you!
published: 16 Jan 2023 -
Kernel and Range
We show, step-by-step, how to find the kernel, nullity, range and rank of a linear transformation. You can find the written version of this post at https://dralb.com/2019/08/02/kernel-and-range/ More Linear Algebra help can be found at https://www.youtube.com/playlist?list=PLC9FwwSK8YlFA7raFGHXm8EVKM0lwzjGM
published: 05 Aug 2019 -
Given a linear transformation, find the kernel and range
published: 24 Jun 2021 -
A Kernel Of A Matrix: An In-Depth Guide To The Concept.
The concept of kernel is quite often explained with the help of a matrix. While it can be a great reference tool, it doesn’t always give an accurate depiction of the concept. In this article, we will learn about kernels using a more detailed and practical example. The problem with Matrices is that they usually involve too many concepts at once. That makes them hard to understand for beginners. In this guide, we will try and explain the concept in a detailed manner that is easy to understand without losing any of the important details.
published: 12 Jun 2019 -
49 - Ker(T) and Im(T)
Algebra 1M - international Course no. 104016 Dr. Aviv Censor Technion - International school of engineering
published: 26 Nov 2015
5:35
Image and Kernel
- Order: Reorder
- Duration: 5:35
- Uploaded Date: 29 May 2019
- views: 175038
Now that we've learned about linear transformations, we can combine this with what we know about vector spaces to learn about the concepts of image and kernel. ...
Now that we've learned about linear transformations, we can combine this with what we know about vector spaces to learn about the concepts of image and kernel. Let's get a closer look!
Script by Howard Whittle
Watch the whole Mathematics playlist: http://bit.ly/ProfDaveMath
Classical Physics Tutorials: http://bit.ly/ProfDavePhysics1
Modern Physics Tutorials: http://bit.ly/ProfDavePhysics2
General Chemistry Tutorials: http://bit.ly/ProfDaveGenChem
Organic Chemistry Tutorials: http://bit.ly/ProfDaveOrgChem
Biochemistry Tutorials: http://bit.ly/ProfDaveBiochem
Biology Tutorials: http://bit.ly/ProfDaveBio
EMAIL► [email protected]
PATREON► http://patreon.com/ProfessorDaveExplains
Check out "Is This Wi-Fi Organic?", my book on disarming pseudoscience!
Amazon: https://amzn.to/2HtNpVH
Bookshop: https://bit.ly/39cKADM
Barnes and Noble: https://bit.ly/3pUjmrn
Book Depository: http://bit.ly/3aOVDlT
https://wn.com/Image_And_Kernel
Now that we've learned about linear transformations, we can combine this with what we know about vector spaces to learn about the concepts of image and kernel. Let's get a closer look!
Script by Howard Whittle
Watch the whole Mathematics playlist: http://bit.ly/ProfDaveMath
Classical Physics Tutorials: http://bit.ly/ProfDavePhysics1
Modern Physics Tutorials: http://bit.ly/ProfDavePhysics2
General Chemistry Tutorials: http://bit.ly/ProfDaveGenChem
Organic Chemistry Tutorials: http://bit.ly/ProfDaveOrgChem
Biochemistry Tutorials: http://bit.ly/ProfDaveBiochem
Biology Tutorials: http://bit.ly/ProfDaveBio
EMAIL► [email protected]
PATREON► http://patreon.com/ProfessorDaveExplains
Check out "Is This Wi-Fi Organic?", my book on disarming pseudoscience!
Amazon: https://amzn.to/2HtNpVH
Bookshop: https://bit.ly/39cKADM
Barnes and Noble: https://bit.ly/3pUjmrn
Book Depository: http://bit.ly/3aOVDlT
8:46
KERNEL and RANGE of a LINEAR TRANSFORMATION - LINEAR ALGEBRA
- Order: Reorder
- Duration: 8:46
- Uploaded Date: 13 May 2016
- views: 267803
We discuss the kernal and range of a linear transformation.
LIKE AND SHARE THE VIDEO IF IT HELPED!
Visit our website: http://bit.ly/1zBPlvm
Subscribe on YouTu...
We discuss the kernal and range of a linear transformation.
LIKE AND SHARE THE VIDEO IF IT HELPED!
Visit our website: http://bit.ly/1zBPlvm
Subscribe on YouTube: http://bit.ly/1vWiRxW
Like us on Facebook: http://on.fb.me/1vWwDRc
Submit your questions on Reddit: http://bit.ly/1GwZZrP
#LinearAlgebra #Algebra #UniversityMath #Lecture
*--Playlists--*
Linear Algebra: https://www.youtube.com/playlist?list=PLDDGPdw7e6AjJacaEe9awozSaOou-NIx_
*--Recommended Textbooks--*
Linear Algebra and Its Applications (Lay): https://amzn.to/37gBZ27
Linear Algebra Done Right (Axler): https://amzn.to/2T0GpBI
Introduction to Linear Algebra (Strang): https://amzn.to/3dC6kJq
Linear Algebra: Step by Step (Singh): https://amzn.to/2T33G65
3,000 Solved Problems in Linear Algebra (Lipschutz): https://amzn.to/3j2nJMw
We discuss the kernel and range of linear transformations, and then prove that the range of a linear transformation is a subspace.
Hello, welcome to TheTrevTutor. I'm here to help you learn your college courses in an easy, efficient manner. If you like what you see, feel free to subscribe and follow me for updates. If you have any questions, leave them below. I try to answer as many questions as possible. If something isn't quite clear or needs more explanation, I can easily make additional videos to satisfy your need for knowledge and understanding.
https://wn.com/Kernel_And_Range_Of_A_Linear_Transformation_Linear_Algebra
We discuss the kernal and range of a linear transformation.
LIKE AND SHARE THE VIDEO IF IT HELPED!
Visit our website: http://bit.ly/1zBPlvm
Subscribe on YouTube: http://bit.ly/1vWiRxW
Like us on Facebook: http://on.fb.me/1vWwDRc
Submit your questions on Reddit: http://bit.ly/1GwZZrP
#LinearAlgebra #Algebra #UniversityMath #Lecture
*--Playlists--*
Linear Algebra: https://www.youtube.com/playlist?list=PLDDGPdw7e6AjJacaEe9awozSaOou-NIx_
*--Recommended Textbooks--*
Linear Algebra and Its Applications (Lay): https://amzn.to/37gBZ27
Linear Algebra Done Right (Axler): https://amzn.to/2T0GpBI
Introduction to Linear Algebra (Strang): https://amzn.to/3dC6kJq
Linear Algebra: Step by Step (Singh): https://amzn.to/2T33G65
3,000 Solved Problems in Linear Algebra (Lipschutz): https://amzn.to/3j2nJMw
We discuss the kernel and range of linear transformations, and then prove that the range of a linear transformation is a subspace.
Hello, welcome to TheTrevTutor. I'm here to help you learn your college courses in an easy, efficient manner. If you like what you see, feel free to subscribe and follow me for updates. If you have any questions, leave them below. I try to answer as many questions as possible. If something isn't quite clear or needs more explanation, I can easily make additional videos to satisfy your need for knowledge and understanding.
- published: 13 May 2016
- views: 267803
2:45
1.6 Ex2 Finding kernel and range
- Order: Reorder
- Duration: 2:45
- Uploaded Date: 31 Oct 2016
- views: 104621
- published: 31 Oct 2016
- views: 104621
12:09
Inverse matrices, column space and null space | Chapter 7, Essence of linear algebra
- Order: Reorder
- Duration: 12:09
- Uploaded Date: 15 Aug 2016
- views: 3119170
How to think about linear systems of equations geometrically.
Help fund future projects: https://www.patreon.com/3blue1brown
An equally valuable form of support...
How to think about linear systems of equations geometrically.
Help fund future projects: https://www.patreon.com/3blue1brown
An equally valuable form of support is to simply share some of the videos.
Home page: https://www.3blue1brown.com/
Full series: http://3b1b.co/eola
Future series like this are funded by the community, through Patreon, where supporters get early access as the series is being produced.
http://3b1b.co/support
Thanks to these viewers for their contributions to translations
Hebrew: Omer Tuchfeld
------------------
3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that).
If you are new to this channel and want to see more, a good place to start is this playlist: https://goo.gl/WmnCQZ
Various social media stuffs:
Website: https://www.3blue1brown.com
Twitter: https://twitter.com/3Blue1Brown
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown
Reddit: https://www.reddit.com/r/3Blue1Brown
https://wn.com/Inverse_Matrices,_Column_Space_And_Null_Space_|_Chapter_7,_Essence_Of_Linear_Algebra
How to think about linear systems of equations geometrically.
Help fund future projects: https://www.patreon.com/3blue1brown
An equally valuable form of support is to simply share some of the videos.
Home page: https://www.3blue1brown.com/
Full series: http://3b1b.co/eola
Future series like this are funded by the community, through Patreon, where supporters get early access as the series is being produced.
http://3b1b.co/support
Thanks to these viewers for their contributions to translations
Hebrew: Omer Tuchfeld
------------------
3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that).
If you are new to this channel and want to see more, a good place to start is this playlist: https://goo.gl/WmnCQZ
Various social media stuffs:
Website: https://www.3blue1brown.com
Twitter: https://twitter.com/3Blue1Brown
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown
Reddit: https://www.reddit.com/r/3Blue1Brown
- published: 15 Aug 2016
- views: 3119170
15:23
Preimage and kernel example | Matrix transformations | Linear Algebra | Khan Academy
- Order: Reorder
- Duration: 15:23
- Uploaded Date: 22 Oct 2009
- views: 232992
Example involving the preimage of a set under a transformation. Definition of kernel of a transformation.
Watch the next lesson: https://www.khanacademy.org/ma...
Example involving the preimage of a set under a transformation. Definition of kernel of a transformation.
Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/linear_transformations/v/sums-and-scalar-multiples-of-linear-transformations?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra
Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/matrix_transformations/linear_transformations/v/preimage-of-a-set?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra
Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to KhanAcademy’s Linear Algebra channel:: https://www.youtube.com/channel/UCGYSKl6e3HM0PP7QR35Crug?sub_confirmation=1
Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy
https://wn.com/Preimage_And_Kernel_Example_|_Matrix_Transformations_|_Linear_Algebra_|_Khan_Academy
Example involving the preimage of a set under a transformation. Definition of kernel of a transformation.
Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/linear_transformations/v/sums-and-scalar-multiples-of-linear-transformations?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra
Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/matrix_transformations/linear_transformations/v/preimage-of-a-set?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra
Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to KhanAcademy’s Linear Algebra channel:: https://www.youtube.com/channel/UCGYSKl6e3HM0PP7QR35Crug?sub_confirmation=1
Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy
- published: 22 Oct 2009
- views: 232992
8:31
Kernel of a matrix - Part 2 | How to determine it! | Linear Algebra | Math2Go
- Order: Reorder
- Duration: 8:31
- Uploaded Date: 16 Jan 2023
- views: 1458
In this video we will look into the kernel of a given matrix / a given linear map. We will learn how to efficiently determine kernels of given matrices.
If you...
In this video we will look into the kernel of a given matrix / a given linear map. We will learn how to efficiently determine kernels of given matrices.
If you want to know more about kernels, see here: https://www.youtube.com/watch?v=fxuI7d32t9o
If you have any questions please feel free to ask. You can also ask for specific other mathematical problems in the comment section below!
Please comment and subscribe if this video was helpful to you!
https://wn.com/Kernel_Of_A_Matrix_Part_2_|_How_To_Determine_It_|_Linear_Algebra_|_Math2Go
In this video we will look into the kernel of a given matrix / a given linear map. We will learn how to efficiently determine kernels of given matrices.
If you want to know more about kernels, see here: https://www.youtube.com/watch?v=fxuI7d32t9o
If you have any questions please feel free to ask. You can also ask for specific other mathematical problems in the comment section below!
Please comment and subscribe if this video was helpful to you!
- published: 16 Jan 2023
- views: 1458
6:25
Kernel and Range
- Order: Reorder
- Duration: 6:25
- Uploaded Date: 05 Aug 2019
- views: 22664
We show, step-by-step, how to find the kernel, nullity, range and rank of a linear transformation.
You can find the written version of this post at
https://dr...
We show, step-by-step, how to find the kernel, nullity, range and rank of a linear transformation.
You can find the written version of this post at
https://dralb.com/2019/08/02/kernel-and-range/
More Linear Algebra help can be found at
https://www.youtube.com/playlist?list=PLC9FwwSK8YlFA7raFGHXm8EVKM0lwzjGM
https://wn.com/Kernel_And_Range
We show, step-by-step, how to find the kernel, nullity, range and rank of a linear transformation.
You can find the written version of this post at
https://dralb.com/2019/08/02/kernel-and-range/
More Linear Algebra help can be found at
https://www.youtube.com/playlist?list=PLC9FwwSK8YlFA7raFGHXm8EVKM0lwzjGM
- published: 05 Aug 2019
- views: 22664
8:25
Given a linear transformation, find the kernel and range
- Order: Reorder
- Duration: 8:25
- Uploaded Date: 24 Jun 2021
- views: 86305
- published: 24 Jun 2021
- views: 86305
8:46
A Kernel Of A Matrix: An In-Depth Guide To The Concept.
- Order: Reorder
- Duration: 8:46
- Uploaded Date: 12 Jun 2019
- views: 49335
The concept of kernel is quite often explained with the help of a matrix. While it can be a great reference tool, it doesn’t always give an accurate depiction o...
The concept of kernel is quite often explained with the help of a matrix. While it can be a great reference tool, it doesn’t always give an accurate depiction of the concept. In this article, we will learn about kernels using a more detailed and practical example. The problem with Matrices is that they usually involve too many concepts at once. That makes them hard to understand for beginners. In this guide, we will try and explain the concept in a detailed manner that is easy to understand without losing any of the important details.
https://wn.com/A_Kernel_Of_A_Matrix_An_In_Depth_Guide_To_The_Concept.
The concept of kernel is quite often explained with the help of a matrix. While it can be a great reference tool, it doesn’t always give an accurate depiction of the concept. In this article, we will learn about kernels using a more detailed and practical example. The problem with Matrices is that they usually involve too many concepts at once. That makes them hard to understand for beginners. In this guide, we will try and explain the concept in a detailed manner that is easy to understand without losing any of the important details.
- published: 12 Jun 2019
- views: 49335
34:28
49 - Ker(T) and Im(T)
- Order: Reorder
- Duration: 34:28
- Uploaded Date: 26 Nov 2015
- views: 129551
Algebra 1M - international
Course no. 104016
Dr. Aviv Censor
Technion - International school of engineering
Algebra 1M - international
Course no. 104016
Dr. Aviv Censor
Technion - International school of engineering
https://wn.com/49_Ker(T)_And_Im(T)
Algebra 1M - international
Course no. 104016
Dr. Aviv Censor
Technion - International school of engineering
- published: 26 Nov 2015
- views: 129551
PLAYLIST TIME:
PLAYLIST TIME:
5:35
Image and Kernel
Now that we've learned about linear transformations, we can combine this with what we know...
published: 29 May 2019
Image and Kernel
Image and Kernel
- Report rights infringement
- published: 29 May 2019
- views: 175038
Now that we've learned about linear transformations, we can combine this with what we know about vector spaces to learn about the concepts of image and kernel. Let's get a closer look!
Script by Howard Whittle
Watch the whole Mathematics playlist: http://bit.ly/ProfDaveMath
Classical Physics Tutorials: http://bit.ly/ProfDavePhysics1
Modern Physics Tutorials: http://bit.ly/ProfDavePhysics2
General Chemistry Tutorials: http://bit.ly/ProfDaveGenChem
Organic Chemistry Tutorials: http://bit.ly/ProfDaveOrgChem
Biochemistry Tutorials: http://bit.ly/ProfDaveBiochem
Biology Tutorials: http://bit.ly/ProfDaveBio
EMAIL► [email protected]
PATREON► http://patreon.com/ProfessorDaveExplains
Check out "Is This Wi-Fi Organic?", my book on disarming pseudoscience!
Amazon: https://amzn.to/2HtNpVH
Bookshop: https://bit.ly/39cKADM
Barnes and Noble: https://bit.ly/3pUjmrn
Book Depository: http://bit.ly/3aOVDlT
8:46
KERNEL and RANGE of a LINEAR TRANSFORMATION - LINEAR ALGEBRA
We discuss the kernal and range of a linear transformation.
LIKE AND SHARE THE VIDEO IF I...
published: 13 May 2016
KERNEL and RANGE of a LINEAR TRANSFORMATION - LINEAR ALGEBRA
KERNEL and RANGE of a LINEAR TRANSFORMATION - LINEAR ALGEBRA
- Report rights infringement
- published: 13 May 2016
- views: 267803
We discuss the kernal and range of a linear transformation.
LIKE AND SHARE THE VIDEO IF IT HELPED!
Visit our website: http://bit.ly/1zBPlvm
Subscribe on YouTube: http://bit.ly/1vWiRxW
Like us on Facebook: http://on.fb.me/1vWwDRc
Submit your questions on Reddit: http://bit.ly/1GwZZrP
#LinearAlgebra #Algebra #UniversityMath #Lecture
*--Playlists--*
Linear Algebra: https://www.youtube.com/playlist?list=PLDDGPdw7e6AjJacaEe9awozSaOou-NIx_
*--Recommended Textbooks--*
Linear Algebra and Its Applications (Lay): https://amzn.to/37gBZ27
Linear Algebra Done Right (Axler): https://amzn.to/2T0GpBI
Introduction to Linear Algebra (Strang): https://amzn.to/3dC6kJq
Linear Algebra: Step by Step (Singh): https://amzn.to/2T33G65
3,000 Solved Problems in Linear Algebra (Lipschutz): https://amzn.to/3j2nJMw
We discuss the kernel and range of linear transformations, and then prove that the range of a linear transformation is a subspace.
Hello, welcome to TheTrevTutor. I'm here to help you learn your college courses in an easy, efficient manner. If you like what you see, feel free to subscribe and follow me for updates. If you have any questions, leave them below. I try to answer as many questions as possible. If something isn't quite clear or needs more explanation, I can easily make additional videos to satisfy your need for knowledge and understanding.
2:45
1.6 Ex2 Finding kernel and range
published: 31 Oct 2016
1.6 Ex2 Finding kernel and range
1.6 Ex2 Finding kernel and range
- Report rights infringement
- published: 31 Oct 2016
- views: 104621
12:09
Inverse matrices, column space and null space | Chapter 7, Essence of linear algebra
How to think about linear systems of equations geometrically.
Help fund future projects: h...
published: 15 Aug 2016
Inverse matrices, column space and null space | Chapter 7, Essence of linear algebra
Inverse matrices, column space and null space | Chapter 7, Essence of linear algebra
- Report rights infringement
- published: 15 Aug 2016
- views: 3119170
How to think about linear systems of equations geometrically.
Help fund future projects: https://www.patreon.com/3blue1brown
An equally valuable form of support is to simply share some of the videos.
Home page: https://www.3blue1brown.com/
Full series: http://3b1b.co/eola
Future series like this are funded by the community, through Patreon, where supporters get early access as the series is being produced.
http://3b1b.co/support
Thanks to these viewers for their contributions to translations
Hebrew: Omer Tuchfeld
------------------
3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that).
If you are new to this channel and want to see more, a good place to start is this playlist: https://goo.gl/WmnCQZ
Various social media stuffs:
Website: https://www.3blue1brown.com
Twitter: https://twitter.com/3Blue1Brown
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown
Reddit: https://www.reddit.com/r/3Blue1Brown
15:23
Preimage and kernel example | Matrix transformations | Linear Algebra | Khan Academy
Example involving the preimage of a set under a transformation. Definition of kernel of a ...
published: 22 Oct 2009
Preimage and kernel example | Matrix transformations | Linear Algebra | Khan Academy
Preimage and kernel example | Matrix transformations | Linear Algebra | Khan Academy
- Report rights infringement
- published: 22 Oct 2009
- views: 232992
Example involving the preimage of a set under a transformation. Definition of kernel of a transformation.
Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/linear_transformations/v/sums-and-scalar-multiples-of-linear-transformations?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra
Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/matrix_transformations/linear_transformations/v/preimage-of-a-set?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra
Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to KhanAcademy’s Linear Algebra channel:: https://www.youtube.com/channel/UCGYSKl6e3HM0PP7QR35Crug?sub_confirmation=1
Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy
8:31
Kernel of a matrix - Part 2 | How to determine it! | Linear Algebra | Math2Go
In this video we will look into the kernel of a given matrix / a given linear map. We will...
published: 16 Jan 2023
Kernel of a matrix - Part 2 | How to determine it! | Linear Algebra | Math2Go
Kernel of a matrix - Part 2 | How to determine it! | Linear Algebra | Math2Go
- Report rights infringement
- published: 16 Jan 2023
- views: 1458
In this video we will look into the kernel of a given matrix / a given linear map. We will learn how to efficiently determine kernels of given matrices.
If you want to know more about kernels, see here: https://www.youtube.com/watch?v=fxuI7d32t9o
If you have any questions please feel free to ask. You can also ask for specific other mathematical problems in the comment section below!
Please comment and subscribe if this video was helpful to you!
6:25
Kernel and Range
We show, step-by-step, how to find the kernel, nullity, range and rank of a linear transfo...
published: 05 Aug 2019
Kernel and Range
Kernel and Range
- Report rights infringement
- published: 05 Aug 2019
- views: 22664
We show, step-by-step, how to find the kernel, nullity, range and rank of a linear transformation.
You can find the written version of this post at
https://dralb.com/2019/08/02/kernel-and-range/
More Linear Algebra help can be found at
https://www.youtube.com/playlist?list=PLC9FwwSK8YlFA7raFGHXm8EVKM0lwzjGM
8:25
Given a linear transformation, find the kernel and range
published: 24 Jun 2021
Given a linear transformation, find the kernel and range
Given a linear transformation, find the kernel and range
- Report rights infringement
- published: 24 Jun 2021
- views: 86305
8:46
A Kernel Of A Matrix: An In-Depth Guide To The Concept.
The concept of kernel is quite often explained with the help of a matrix. While it can be ...
published: 12 Jun 2019
A Kernel Of A Matrix: An In-Depth Guide To The Concept.
A Kernel Of A Matrix: An In-Depth Guide To The Concept.
- Report rights infringement
- published: 12 Jun 2019
- views: 49335
The concept of kernel is quite often explained with the help of a matrix. While it can be a great reference tool, it doesn’t always give an accurate depiction of the concept. In this article, we will learn about kernels using a more detailed and practical example. The problem with Matrices is that they usually involve too many concepts at once. That makes them hard to understand for beginners. In this guide, we will try and explain the concept in a detailed manner that is easy to understand without losing any of the important details.
34:28
49 - Ker(T) and Im(T)
Algebra 1M - international
Course no. 104016
Dr. Aviv Censor
Technion - International scho...
published: 26 Nov 2015
49 - Ker(T) and Im(T)
49 - Ker(T) and Im(T)
- Report rights infringement
- published: 26 Nov 2015
- views: 129551
Algebra 1M - international
Course no. 104016
Dr. Aviv Censor
Technion - International school of engineering
Kernel (linear algebra)
In mathematics, and more specifically in linear algebra and functional analysis, the kernel (also known as null space or nullspace) of a linear map L : V → W between two vector spaces V and W, is the set of all elements v of V for which L(v) = 0, where 0 denotes the zero vector in W. That is, in set-builder notation,
Properties of the Kernel
The kernel of L is a linear subspace of the domain V. In the linear map L : V → W, two elements of V have the same image in W if and only if their difference lies in the kernel of L:
It follows that the image of L is isomorphic to the quotient of V by the kernel:
This implies the rank–nullity theorem:
where, by “rank” we mean the dimension of the image of L, and by “nullity” that of the kernel of L.
When V is an inner product space, the quotient V / ker(L) can be identified with the orthogonal complement in V of ker(L). This is the generalization to linear operators of the row space, or coimage, of a matrix.
Application to modules
The notion of kernel applies to the homomorphisms of modules, the latter being a generalization of the vector space over a field to that over a ring. The domain of the mapping is a module, and the kernel constitutes a "submodule". Here, the concepts of rank and nullity do not necessarily apply.
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Kernel_(linear_algebra)
Image and Kernel...
KERNEL and RANGE of a LINEAR TRANSFORMATION - LINE...
1.6 Ex2 Finding kernel and range...
Inverse matrices, column space and null space | Ch...
Preimage and kernel example | Matrix transformatio...
Kernel of a matrix - Part 2 | How to determine it!...
Kernel and Range...
Given a linear transformation, find the kernel and...
A Kernel Of A Matrix: An In-Depth Guide To The Con...