In mathematics, an affine space is a geometric structure that generalizes the properties of Euclidean spaces that are independent of the concepts of distance and measure of angles, keeping only the properties related to parallelism and ratio of lengths for parallel line segments. A Euclidean space is an affine space over the reals, equipped with a metric, the Euclidean distance. Therefore, in Euclidean geometry, an affine property is a property that may be proved in affine spaces.
In an affine space, there is no distinguished point that serves as an origin. Hence, no vector has a fixed origin and no vector can be uniquely associated to a point. In an affine space, there are instead displacement vectors, also called translation vectors or simply translations, between two points of the space. Thus it makes sense to subtract two points of the space, giving a translation vector, but it does not make sense to add two points of the space. Likewise, it makes sense to add a vector to a point of an affine space, resulting in a new point translated from the starting point by that vector.
Join this channel to get access to perks:
https://www.youtube.com/channel/UCSDJ-oyyTfmb-FRuHuNqIcQ/join Linear Algebra : Affine subspaces and affine mappings | By MyCampus | my campus
#mycampus #affinesubspace
#affinemaps
#linearalgebra #mathematics
Notes Link :- https://drive.google.com/file/d/1xC2Roj1s0_5cD1RDWitnrIZVRZcexO8m/view?usp=sharing
Checkout our Other Playlists
Python OPPE PYQ playlist : https://www.youtube.com/playlist?list=PLZd_9NahuB3G50kpQ35Y50Wfkq1q_rUwy
Mathematics 2 for Data Science : https://www.youtube.com/playlist?list=PLZd_9NahuB3EztpCeK9O81agMhePG0hfk
Mathematics 1 for Data Science : https://www.youtube.com/playlist?list=PLZd_9NahuB3G7yNvcyVChnSM29oNYTqwO
Python Sessions : https://www.youtube.com/playlist?list=PLZd_9NahuB3Ew4jc67HUyRpi4yJOhQqDx
ABOUT OUR...
published: 26 Mar 2023
Affine subspaces and transformations - 01 - affine combinations
Affine transformations generalize both linear transformations and equations of the form y=mx+b. They are ubiquitous in, for example, support vector machines from machine learning. In this video, we describe affine combinations algebraically and geometrically.
This is part of a series of lectures on special topics in linear algebra https://www.youtube.com/playlist?list=PLSx1kJDjrLRSS4Aio9WfQlNnH6X6pC_8t. It is assumed the viewer has taken (or is well into) a course in linear algebra. Some topics may also require additional background. Topics covered include linear regression and data analysis, ordinary linear differential equations, differential operators, function spaces, category-theoretic aspects of linear algebra, support vector machines (machine learning), Hamming's error-correcting c...
published: 24 Dec 2019
What is...an affine space?
Goal.
Explaining basic concepts of linear algebra in an intuitive way.
This time.
What is...an affine space? Or: I lost my origin.
Warning.
There is a typo on the fourth slide, as pointed out in the comments. The "green matrix" should be {{-1, 0}, {0, -1}}. Sorry for that.
Slides.
http://www.dtubbenhauer.com/youtube.html
#linearalgebra
#algebra
#mathematics
published: 31 Mar 2021
Affine Space - 1 Minute Intuition & Visualization
Linear Algebra Affine Space in 2D and 3D.
Audio: https://pixabay.com/music/beautiful-plays-reflected-light-147979/
#linearalgebra #manim
published: 08 Dec 2023
Best affine approximation
The derivative can be viewed as providing the best approximating affine map to a function.
Princeton COS 302, Lecture 13, Part 1
published: 25 Mar 2020
Affine subspaces and transformations - 02 - affine subspaces
Affine transformations generalize both linear transformations and equations of the form y=mx+b. They are ubiquitous in support vector machines from machine learning. In this video, we describe the notion of affine span and affine subspaces. Briefly, these are almost geometrically the same as vector subspaces. The one difference is that they do not need to contain the zero vector.
Note: In the definition of affine subspace, the V in the expression "t\vec{u}+(1-t)\vec{v}\in V" should be replaced with A. The affine subspace here is called A.
This is part of a series of lectures on special topics in linear algebra https://www.youtube.com/playlist?list=PLSx1kJDjrLRSS4Aio9WfQlNnH6X6pC_8t. It is assumed the viewer has taken (or is well into) a course in linear algebra. Some topics may also requi...
published: 24 Dec 2019
Barycentric Subspaces and Affine Spans in Manifolds Xavier Pennec
Video shows what affine space means. a vector space having no origin. Affine space Meaning. How to pronounce, definition audio dictionary. How to say affine space. Powered by MaryTTS, Wiktionary
Join this channel to get access to perks:
https://www.youtube.com/channel/UCSDJ-oyyTfmb-FRuHuNqIcQ/join Linear Algebra : Affine subspaces and affine mappings | ...
Join this channel to get access to perks:
https://www.youtube.com/channel/UCSDJ-oyyTfmb-FRuHuNqIcQ/join Linear Algebra : Affine subspaces and affine mappings | By MyCampus | my campus
#mycampus #affinesubspace
#affinemaps
#linearalgebra #mathematics
Notes Link :- https://drive.google.com/file/d/1xC2Roj1s0_5cD1RDWitnrIZVRZcexO8m/view?usp=sharing
Checkout our Other Playlists
Python OPPE PYQ playlist : https://www.youtube.com/playlist?list=PLZd_9NahuB3G50kpQ35Y50Wfkq1q_rUwy
Mathematics 2 for Data Science : https://www.youtube.com/playlist?list=PLZd_9NahuB3EztpCeK9O81agMhePG0hfk
Mathematics 1 for Data Science : https://www.youtube.com/playlist?list=PLZd_9NahuB3G7yNvcyVChnSM29oNYTqwO
Python Sessions : https://www.youtube.com/playlist?list=PLZd_9NahuB3Ew4jc67HUyRpi4yJOhQqDx
ABOUT OUR CHANNEL
Our channel is about Teaching and Exploring. We cover lots of cool stuff such as Data science, Machine learning and Coding
Check out our channel here:
https://www.youtube.com/data_matrix
Don’t forget to subscribe!
GET IN TOUCH
Contact us on [email protected]
FOLLOW US ON SOCIAL
Get updates or reach out to Get updates on our Social Media Profiles!
Facebook: https://facebook.com/rishu.rajgautam56
Instagram: https://Instagram.com/rishu_raj_gautam
LinkedIn: https://www.linkedin.com/in/rishurajgautam Telegram Group link :-
https://t.me/MycampusByRishu
Join this channel to get access to perks:
https://www.youtube.com/channel/UCSDJ-oyyTfmb-FRuHuNqIcQ/join Linear Algebra : Affine subspaces and affine mappings | By MyCampus | my campus
#mycampus #affinesubspace
#affinemaps
#linearalgebra #mathematics
Notes Link :- https://drive.google.com/file/d/1xC2Roj1s0_5cD1RDWitnrIZVRZcexO8m/view?usp=sharing
Checkout our Other Playlists
Python OPPE PYQ playlist : https://www.youtube.com/playlist?list=PLZd_9NahuB3G50kpQ35Y50Wfkq1q_rUwy
Mathematics 2 for Data Science : https://www.youtube.com/playlist?list=PLZd_9NahuB3EztpCeK9O81agMhePG0hfk
Mathematics 1 for Data Science : https://www.youtube.com/playlist?list=PLZd_9NahuB3G7yNvcyVChnSM29oNYTqwO
Python Sessions : https://www.youtube.com/playlist?list=PLZd_9NahuB3Ew4jc67HUyRpi4yJOhQqDx
ABOUT OUR CHANNEL
Our channel is about Teaching and Exploring. We cover lots of cool stuff such as Data science, Machine learning and Coding
Check out our channel here:
https://www.youtube.com/data_matrix
Don’t forget to subscribe!
GET IN TOUCH
Contact us on [email protected]
FOLLOW US ON SOCIAL
Get updates or reach out to Get updates on our Social Media Profiles!
Facebook: https://facebook.com/rishu.rajgautam56
Instagram: https://Instagram.com/rishu_raj_gautam
LinkedIn: https://www.linkedin.com/in/rishurajgautam Telegram Group link :-
https://t.me/MycampusByRishu
Affine transformations generalize both linear transformations and equations of the form y=mx+b. They are ubiquitous in, for example, support vector machines fro...
Affine transformations generalize both linear transformations and equations of the form y=mx+b. They are ubiquitous in, for example, support vector machines from machine learning. In this video, we describe affine combinations algebraically and geometrically.
This is part of a series of lectures on special topics in linear algebra https://www.youtube.com/playlist?list=PLSx1kJDjrLRSS4Aio9WfQlNnH6X6pC_8t. It is assumed the viewer has taken (or is well into) a course in linear algebra. Some topics may also require additional background. Topics covered include linear regression and data analysis, ordinary linear differential equations, differential operators, function spaces, category-theoretic aspects of linear algebra, support vector machines (machine learning), Hamming's error-correcting codes, stochastic maps and Markov chains, tensor products, finite-dimensional C*-algebras, algebraic probability theory, completely positive maps, aspects of quantum information theory, and more.
The next video on Special Topics in Linear Algebra is on affine subspaces: https://youtu.be/ErCl7PCkoyc
These videos were created during the 2019 Spring/Summer semester at the UConn CETL Lightboard Room.
Affine transformations generalize both linear transformations and equations of the form y=mx+b. They are ubiquitous in, for example, support vector machines from machine learning. In this video, we describe affine combinations algebraically and geometrically.
This is part of a series of lectures on special topics in linear algebra https://www.youtube.com/playlist?list=PLSx1kJDjrLRSS4Aio9WfQlNnH6X6pC_8t. It is assumed the viewer has taken (or is well into) a course in linear algebra. Some topics may also require additional background. Topics covered include linear regression and data analysis, ordinary linear differential equations, differential operators, function spaces, category-theoretic aspects of linear algebra, support vector machines (machine learning), Hamming's error-correcting codes, stochastic maps and Markov chains, tensor products, finite-dimensional C*-algebras, algebraic probability theory, completely positive maps, aspects of quantum information theory, and more.
The next video on Special Topics in Linear Algebra is on affine subspaces: https://youtu.be/ErCl7PCkoyc
These videos were created during the 2019 Spring/Summer semester at the UConn CETL Lightboard Room.
Goal.
Explaining basic concepts of linear algebra in an intuitive way.
This time.
What is...an affine space? Or: I lost my origin.
Warning.
There is a typo ...
Goal.
Explaining basic concepts of linear algebra in an intuitive way.
This time.
What is...an affine space? Or: I lost my origin.
Warning.
There is a typo on the fourth slide, as pointed out in the comments. The "green matrix" should be {{-1, 0}, {0, -1}}. Sorry for that.
Slides.
http://www.dtubbenhauer.com/youtube.html
#linearalgebra
#algebra
#mathematics
Goal.
Explaining basic concepts of linear algebra in an intuitive way.
This time.
What is...an affine space? Or: I lost my origin.
Warning.
There is a typo on the fourth slide, as pointed out in the comments. The "green matrix" should be {{-1, 0}, {0, -1}}. Sorry for that.
Slides.
http://www.dtubbenhauer.com/youtube.html
#linearalgebra
#algebra
#mathematics
Affine transformations generalize both linear transformations and equations of the form y=mx+b. They are ubiquitous in support vector machines from machine lear...
Affine transformations generalize both linear transformations and equations of the form y=mx+b. They are ubiquitous in support vector machines from machine learning. In this video, we describe the notion of affine span and affine subspaces. Briefly, these are almost geometrically the same as vector subspaces. The one difference is that they do not need to contain the zero vector.
Note: In the definition of affine subspace, the V in the expression "t\vec{u}+(1-t)\vec{v}\in V" should be replaced with A. The affine subspace here is called A.
This is part of a series of lectures on special topics in linear algebra https://www.youtube.com/playlist?list=PLSx1kJDjrLRSS4Aio9WfQlNnH6X6pC_8t. It is assumed the viewer has taken (or is well into) a course in linear algebra. Some topics may also require additional background. Topics covered include linear regression and data analysis, ordinary linear differential equations, differential operators, function spaces, category-theoretic aspects of linear algebra, support vector machines (machine learning), Hamming's error-correcting codes, stochastic maps and Markov chains, tensor products, finite-dimensional C*-algebras, algebraic probability theory, completely positive maps, aspects of quantum information theory, and more.
The next video on Special Topics in Linear Algebra is on affine transformations: https://youtu.be/PVhgAbh01ks
The previous video on Special Topics in Linear Algebra is on affine combinations: https://youtu.be/fWRm9dISpNk
These videos were created during the 2019 Spring/Summer semester at the UConn CETL Lightboard Room.
Affine transformations generalize both linear transformations and equations of the form y=mx+b. They are ubiquitous in support vector machines from machine learning. In this video, we describe the notion of affine span and affine subspaces. Briefly, these are almost geometrically the same as vector subspaces. The one difference is that they do not need to contain the zero vector.
Note: In the definition of affine subspace, the V in the expression "t\vec{u}+(1-t)\vec{v}\in V" should be replaced with A. The affine subspace here is called A.
This is part of a series of lectures on special topics in linear algebra https://www.youtube.com/playlist?list=PLSx1kJDjrLRSS4Aio9WfQlNnH6X6pC_8t. It is assumed the viewer has taken (or is well into) a course in linear algebra. Some topics may also require additional background. Topics covered include linear regression and data analysis, ordinary linear differential equations, differential operators, function spaces, category-theoretic aspects of linear algebra, support vector machines (machine learning), Hamming's error-correcting codes, stochastic maps and Markov chains, tensor products, finite-dimensional C*-algebras, algebraic probability theory, completely positive maps, aspects of quantum information theory, and more.
The next video on Special Topics in Linear Algebra is on affine transformations: https://youtu.be/PVhgAbh01ks
The previous video on Special Topics in Linear Algebra is on affine combinations: https://youtu.be/fWRm9dISpNk
These videos were created during the 2019 Spring/Summer semester at the UConn CETL Lightboard Room.
Video shows what affine space means. a vector space having no origin. Affine space Meaning. How to pronounce, definition audio dictionary. How to say affine sp...
Video shows what affine space means. a vector space having no origin. Affine space Meaning. How to pronounce, definition audio dictionary. How to say affine space. Powered by MaryTTS, Wiktionary
Video shows what affine space means. a vector space having no origin. Affine space Meaning. How to pronounce, definition audio dictionary. How to say affine space. Powered by MaryTTS, Wiktionary
Join this channel to get access to perks:
https://www.youtube.com/channel/UCSDJ-oyyTfmb-FRuHuNqIcQ/join Linear Algebra : Affine subspaces and affine mappings | By MyCampus | my campus
#mycampus #affinesubspace
#affinemaps
#linearalgebra #mathematics
Notes Link :- https://drive.google.com/file/d/1xC2Roj1s0_5cD1RDWitnrIZVRZcexO8m/view?usp=sharing
Checkout our Other Playlists
Python OPPE PYQ playlist : https://www.youtube.com/playlist?list=PLZd_9NahuB3G50kpQ35Y50Wfkq1q_rUwy
Mathematics 2 for Data Science : https://www.youtube.com/playlist?list=PLZd_9NahuB3EztpCeK9O81agMhePG0hfk
Mathematics 1 for Data Science : https://www.youtube.com/playlist?list=PLZd_9NahuB3G7yNvcyVChnSM29oNYTqwO
Python Sessions : https://www.youtube.com/playlist?list=PLZd_9NahuB3Ew4jc67HUyRpi4yJOhQqDx
ABOUT OUR CHANNEL
Our channel is about Teaching and Exploring. We cover lots of cool stuff such as Data science, Machine learning and Coding
Check out our channel here:
https://www.youtube.com/data_matrix
Don’t forget to subscribe!
GET IN TOUCH
Contact us on [email protected]
FOLLOW US ON SOCIAL
Get updates or reach out to Get updates on our Social Media Profiles!
Facebook: https://facebook.com/rishu.rajgautam56
Instagram: https://Instagram.com/rishu_raj_gautam
LinkedIn: https://www.linkedin.com/in/rishurajgautam Telegram Group link :-
https://t.me/MycampusByRishu
Affine transformations generalize both linear transformations and equations of the form y=mx+b. They are ubiquitous in, for example, support vector machines from machine learning. In this video, we describe affine combinations algebraically and geometrically.
This is part of a series of lectures on special topics in linear algebra https://www.youtube.com/playlist?list=PLSx1kJDjrLRSS4Aio9WfQlNnH6X6pC_8t. It is assumed the viewer has taken (or is well into) a course in linear algebra. Some topics may also require additional background. Topics covered include linear regression and data analysis, ordinary linear differential equations, differential operators, function spaces, category-theoretic aspects of linear algebra, support vector machines (machine learning), Hamming's error-correcting codes, stochastic maps and Markov chains, tensor products, finite-dimensional C*-algebras, algebraic probability theory, completely positive maps, aspects of quantum information theory, and more.
The next video on Special Topics in Linear Algebra is on affine subspaces: https://youtu.be/ErCl7PCkoyc
These videos were created during the 2019 Spring/Summer semester at the UConn CETL Lightboard Room.
Goal.
Explaining basic concepts of linear algebra in an intuitive way.
This time.
What is...an affine space? Or: I lost my origin.
Warning.
There is a typo on the fourth slide, as pointed out in the comments. The "green matrix" should be {{-1, 0}, {0, -1}}. Sorry for that.
Slides.
http://www.dtubbenhauer.com/youtube.html
#linearalgebra
#algebra
#mathematics
Affine transformations generalize both linear transformations and equations of the form y=mx+b. They are ubiquitous in support vector machines from machine learning. In this video, we describe the notion of affine span and affine subspaces. Briefly, these are almost geometrically the same as vector subspaces. The one difference is that they do not need to contain the zero vector.
Note: In the definition of affine subspace, the V in the expression "t\vec{u}+(1-t)\vec{v}\in V" should be replaced with A. The affine subspace here is called A.
This is part of a series of lectures on special topics in linear algebra https://www.youtube.com/playlist?list=PLSx1kJDjrLRSS4Aio9WfQlNnH6X6pC_8t. It is assumed the viewer has taken (or is well into) a course in linear algebra. Some topics may also require additional background. Topics covered include linear regression and data analysis, ordinary linear differential equations, differential operators, function spaces, category-theoretic aspects of linear algebra, support vector machines (machine learning), Hamming's error-correcting codes, stochastic maps and Markov chains, tensor products, finite-dimensional C*-algebras, algebraic probability theory, completely positive maps, aspects of quantum information theory, and more.
The next video on Special Topics in Linear Algebra is on affine transformations: https://youtu.be/PVhgAbh01ks
The previous video on Special Topics in Linear Algebra is on affine combinations: https://youtu.be/fWRm9dISpNk
These videos were created during the 2019 Spring/Summer semester at the UConn CETL Lightboard Room.
Video shows what affine space means. a vector space having no origin. Affine space Meaning. How to pronounce, definition audio dictionary. How to say affine space. Powered by MaryTTS, Wiktionary
In mathematics, an affine space is a geometric structure that generalizes the properties of Euclidean spaces that are independent of the concepts of distance and measure of angles, keeping only the properties related to parallelism and ratio of lengths for parallel line segments. A Euclidean space is an affine space over the reals, equipped with a metric, the Euclidean distance. Therefore, in Euclidean geometry, an affine property is a property that may be proved in affine spaces.
In an affine space, there is no distinguished point that serves as an origin. Hence, no vector has a fixed origin and no vector can be uniquely associated to a point. In an affine space, there are instead displacement vectors, also called translation vectors or simply translations, between two points of the space. Thus it makes sense to subtract two points of the space, giving a translation vector, but it does not make sense to add two points of the space. Likewise, it makes sense to add a vector to a point of an affine space, resulting in a new point translated from the starting point by that vector.