These elements are "special" in that they fall on a subvariety of the general linear group – they satisfy a polynomial equation (since the determinant is polynomial in the entries).
Geometric interpretation
The special linear group SL(n, R) can be characterized as the group of volume and orientation preserving linear transformations of Rn; this corresponds to the interpretation of the determinant as measuring change in volume and orientation.
Lie subgroup
When F is R or C, SL(n, F) is a Lie subgroup of GL(n, F) of dimension n2 − 1. The Lie algebra of SL(n, F) consists of all n × n matrices over F with vanishing trace. The Lie bracket is given by the commutator.
Linear was formed in 1988 in Sunrise, Florida after Pennachio and Tolga Katas finished the recording of "Sending All My Love" and released it on their record label, Futura Records.
Linear started out as Charlie Pennachio only, before Wyatt Pauley (bass), Phil Conneilly (guitar), Gerald "Pee Wee" Rappaport (drums) and Joe Restivo (bongos) were asked to join the band. Rappaport and Conneilly stepped down from the lineup in late 1989.
Charlie Pennachio was an original member of freestyle artist Stevie B and Tolga Katas' Miami crew band. Pennachio's first CD was produced and written by himself and Katas, and released under their own label, Futura International Records. Listener reaction was overboard and the single entered the national pop charts in the US. Atlantic Records caught wind of the single and tracked Pennachio down, and soon signed him to a recording contract. "Sending All My Love" soared into the U.S. Top 5 and earned RIAA Platinum certification.
In mathematics, a matrix group is a groupG consisting of invertiblematrices over some fieldK, usually fixed in advance, with operations of matrix multiplication and inversion. More generally, one can consider n×n matrices over a commutativeringR. (The size of the matrices is restricted to be finite, as any group can be represented as a group of infinite matrices over any field.) A linear group is an abstract group that is isomorphic to a matrix group over a field K, in other words, admitting a faithful, finite-dimensional representation over K.
Any finite group is linear, because it can be realized by permutation matrices using Cayley's theorem. Among infinite groups, linear groups form an interesting and tractable class. Examples of groups that are not linear include all "sufficiently large" groups; for example, the infinite symmetric group of permutations of an infinite set.
Basic examples
The set MR(n,n) of n×n matrices over a commutative ringR is itself a ring under matrix addition and multiplication. The group of units of MR(n,n) is called the general linear group of n×n matrices over the ring R and is denoted GLn(R) or GL(n,R). All matrix groups are subgroups of some general linear group.
Matrices are a great example of infinite, nonabelian groups. Here we introduce matrix groups with an emphasis on the general linear group and special linear group. The general linear group is written as GLn(F), where F is the field used for the matrix elements. The most common examples are GLn(R) and GLn(C). Similarly, the special linear group is written as SLn.
Be sure to subscribe so you don't miss new lessons from Socratica:
http://bit.ly/1ixuu9W
♦♦♦♦♦♦♦♦♦♦
We recommend the following textbooks:
Dummit & Foote, Abstract Algebra 3rd Edition
http://amzn.to/2oOBd5S
Milne, Algebra Course Notes (available free online)
http://www.jmilne.org/math/CourseNotes/index.html
♦♦♦♦♦♦♦♦♦♦
Ways to support our channel:
► Join our Patreon : https://www.patreon.com/socratica
► Make a one-ti...
published: 14 Apr 2014
The General Linear Group, The Special Linear Group, The Group C^n with Componentwise Multiplication
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys
The General Linear Group, The Special Linear Group, The Group C^n with Componentwise Multiplication
published: 01 Nov 2018
Group, Aux, Matrix: What's The Difference?
It was a long time after I started mixing audio that I really learned what the difference between a group, an aux, and a matrix was. They all process and route audio, but in different ways, so it's easy to get them confused and not know which one to use for which application. In this video, I'll teach you the difference between them and give you practical applications for each one. Hope this helps!
Also, don't forget to get your FREE "7 Step Mix" download!
https://www.themixingprocess.com/
- Schuyler
published: 17 Sep 2022
Group Theory| Lecture 11| Set of matrices is an abelian group under matrix addition |Theta Classes
In this lecture we are taking set of matrices as a set and with this set we are going to show it is an abelian group under matrix addition. Firstly we will take matrix of order 2 and we will show that this collection of matrices satisfies all the properties of a group with the operation of matrix addition .After this we will take a general case in which we will consider a set of all matrices of any dimension and we prove it that this set is also an abelian group under matrix addition.
If anyone has any doubt regarding this lecture do mention it in the comment section.
Keep connected with Theta Classes to study various topics of higher mathematics.
published: 23 May 2022
Tanja Savic x Corona - Laga Laga - (Mashup) - Alexandra & Matrix Band vs Joce Panov
ALEXANDRA on Instagram:
https://www.instagram.com/alexandra.matrix/
ALEXANDRA ON TIK TOK:
https://www.tiktok.com/@alexandra.matrix
✔ Social Media:
https://emdc.yt/alexandramatrix
✔ Stream & Download:
https://emdc.yt/lagalaga
MANAGER: +38765598621 – RAJKO JOVANIC
Alexandra & Matrix Band Official Youtube Channel
Recording, Mix & Master: Filip Mladenovic - One Music
Video by: TOXIC
Zabranjeno svako kopiranje video i/ili audio snimaka i postavljanje na druge kanale!
Marketing:
UNDER CONTROL
Marketing Management
BLKN +387 65 598 621
EU +49 176 432696 01
Mail: [email protected]
Web: www.underctrl.de
Distributed by: EMDC ®
⏩ EMDC Network: https://emdcnetwork.com
(YouTube MCN, Digitalni marketing i all-round usluge)
🔊 EMDC Music: https://emdcmusic.com
(Platforma za di...
published: 15 Sep 2019
What are...matrix groups?
Goal.
Explaining basic concepts of (a classical course in) algebra in an intuitive way.
This time.
What are...matrix groups? Or: The most important groups?!
Disclaimer.
Nobody is perfect, and I might have said something silly. If there is any doubt, then please check the references.
Slides.
http://www.dtubbenhauer.com/youtube.html
Material used.
https://en.wikipedia.org/wiki/General_linear_group
https://en.wikipedia.org/wiki/Linear_group
https://en.wikipedia.org/wiki/Automorphism_group
https://en.wikipedia.org/wiki/Special_linear_group
Multiplication table of SL2(F3).
https://en.wikipedia.org/wiki/Special_linear_group#/media/File:SL(2,3);_Cayley_table.svg
Periodic table.
https://irandrus.files.wordpress.com/2012/06/periodic-table-of-groups.pdf
Mathematica.
https://demonstrations....
published: 23 May 2021
Lec - 38 General Linear Group or Matrix Group | IIT JAM | CSIR UGC NET | GATE MA | B Sc
Collection of all non-singular matrices, whose elements are taken from a field.
#generallineargroup
#matrixgroup
#groupofmatrices
#grouptheory
#abstractalgebra
published: 08 Dec 2017
Group Theory|Lecture 8 Group of Matrices|Is set of 2*2 matrices over Z form a group under addition?
published: 03 Apr 2020
The Classical Matrix Groups
In this video, we survey the classical matrix groups, namely the general linear group, the special linear group, the orthogonal group, the special orthogonal group, the unitary group, the special unitary group, and the sympletic group. We briefly discuss their importance to geometry, simple groups, and physical science.
This is lecture 35 (part 1/3) of the lecture series offered by Dr. Andrew Misseldine for the course Math 4220 - Abstract Algebra I at Southern Utah University. A transcript of this lecture can be found at Dr. Misseldine's website or through his Google Drive at:
https://drive.google.com/file/d/1V9Pt3zBqYWkccHWVvPqPocwhyWBorp72/view
This lecture is based upon Section 12.1 of Abstract Algebra: Theory and Applications (http://abstract.ups.edu/) by Tom Judson. Please post any...
Matrices are a great example of infinite, nonabelian groups. Here we introduce matrix groups with an emphasis on the general linear group and special linear gr...
Matrices are a great example of infinite, nonabelian groups. Here we introduce matrix groups with an emphasis on the general linear group and special linear group. The general linear group is written as GLn(F), where F is the field used for the matrix elements. The most common examples are GLn(R) and GLn(C). Similarly, the special linear group is written as SLn.
Be sure to subscribe so you don't miss new lessons from Socratica:
http://bit.ly/1ixuu9W
♦♦♦♦♦♦♦♦♦♦
We recommend the following textbooks:
Dummit & Foote, Abstract Algebra 3rd Edition
http://amzn.to/2oOBd5S
Milne, Algebra Course Notes (available free online)
http://www.jmilne.org/math/CourseNotes/index.html
♦♦♦♦♦♦♦♦♦♦
Ways to support our channel:
► Join our Patreon : https://www.patreon.com/socratica
► Make a one-time PayPal donation: https://www.paypal.me/socratica
► We also accept Bitcoin @ 1EttYyGwJmpy9bLY2UcmEqMJuBfaZ1HdG9
Thank you!
♦♦♦♦♦♦♦♦♦♦
Connect with us!
Facebook: https://www.facebook.com/SocraticaStudios/
Instagram: https://www.instagram.com/SocraticaStudios/
Twitter: https://twitter.com/Socratica
♦♦♦♦♦♦♦♦♦♦
Teaching Assistant: Liliana de Castro
Written & Directed by Michael Harrison
Produced by Kimberly Hatch Harrison
♦♦♦♦♦♦♦♦♦♦
Matrices are a great example of infinite, nonabelian groups. Here we introduce matrix groups with an emphasis on the general linear group and special linear group. The general linear group is written as GLn(F), where F is the field used for the matrix elements. The most common examples are GLn(R) and GLn(C). Similarly, the special linear group is written as SLn.
Be sure to subscribe so you don't miss new lessons from Socratica:
http://bit.ly/1ixuu9W
♦♦♦♦♦♦♦♦♦♦
We recommend the following textbooks:
Dummit & Foote, Abstract Algebra 3rd Edition
http://amzn.to/2oOBd5S
Milne, Algebra Course Notes (available free online)
http://www.jmilne.org/math/CourseNotes/index.html
♦♦♦♦♦♦♦♦♦♦
Ways to support our channel:
► Join our Patreon : https://www.patreon.com/socratica
► Make a one-time PayPal donation: https://www.paypal.me/socratica
► We also accept Bitcoin @ 1EttYyGwJmpy9bLY2UcmEqMJuBfaZ1HdG9
Thank you!
♦♦♦♦♦♦♦♦♦♦
Connect with us!
Facebook: https://www.facebook.com/SocraticaStudios/
Instagram: https://www.instagram.com/SocraticaStudios/
Twitter: https://twitter.com/Socratica
♦♦♦♦♦♦♦♦♦♦
Teaching Assistant: Liliana de Castro
Written & Directed by Michael Harrison
Produced by Kimberly Hatch Harrison
♦♦♦♦♦♦♦♦♦♦
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys
The General Linear Group, The Special Linear Group, The Group C^n with Componentwise Multiplication
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys
The General Linear Group, The Special Linear Group, The Group C^n with Componentwise Multiplication
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys
The General Linear Group, The Special Linear Group, The Group C^n with Componentwise Multiplication
It was a long time after I started mixing audio that I really learned what the difference between a group, an aux, and a matrix was. They all process and route ...
It was a long time after I started mixing audio that I really learned what the difference between a group, an aux, and a matrix was. They all process and route audio, but in different ways, so it's easy to get them confused and not know which one to use for which application. In this video, I'll teach you the difference between them and give you practical applications for each one. Hope this helps!
Also, don't forget to get your FREE "7 Step Mix" download!
https://www.themixingprocess.com/
- Schuyler
It was a long time after I started mixing audio that I really learned what the difference between a group, an aux, and a matrix was. They all process and route audio, but in different ways, so it's easy to get them confused and not know which one to use for which application. In this video, I'll teach you the difference between them and give you practical applications for each one. Hope this helps!
Also, don't forget to get your FREE "7 Step Mix" download!
https://www.themixingprocess.com/
- Schuyler
In this lecture we are taking set of matrices as a set and with this set we are going to show it is an abelian group under matrix addition. Firstly we will take...
In this lecture we are taking set of matrices as a set and with this set we are going to show it is an abelian group under matrix addition. Firstly we will take matrix of order 2 and we will show that this collection of matrices satisfies all the properties of a group with the operation of matrix addition .After this we will take a general case in which we will consider a set of all matrices of any dimension and we prove it that this set is also an abelian group under matrix addition.
If anyone has any doubt regarding this lecture do mention it in the comment section.
Keep connected with Theta Classes to study various topics of higher mathematics.
In this lecture we are taking set of matrices as a set and with this set we are going to show it is an abelian group under matrix addition. Firstly we will take matrix of order 2 and we will show that this collection of matrices satisfies all the properties of a group with the operation of matrix addition .After this we will take a general case in which we will consider a set of all matrices of any dimension and we prove it that this set is also an abelian group under matrix addition.
If anyone has any doubt regarding this lecture do mention it in the comment section.
Keep connected with Theta Classes to study various topics of higher mathematics.
ALEXANDRA on Instagram:
https://www.instagram.com/alexandra.matrix/
ALEXANDRA ON TIK TOK:
https://www.tiktok.com/@alexandra.matrix
✔ Social Media:
https://em...
ALEXANDRA on Instagram:
https://www.instagram.com/alexandra.matrix/
ALEXANDRA ON TIK TOK:
https://www.tiktok.com/@alexandra.matrix
✔ Social Media:
https://emdc.yt/alexandramatrix
✔ Stream & Download:
https://emdc.yt/lagalaga
MANAGER: +38765598621 – RAJKO JOVANIC
Alexandra & Matrix Band Official Youtube Channel
Recording, Mix & Master: Filip Mladenovic - One Music
Video by: TOXIC
Zabranjeno svako kopiranje video i/ili audio snimaka i postavljanje na druge kanale!
Marketing:
UNDER CONTROL
Marketing Management
BLKN +387 65 598 621
EU +49 176 432696 01
Mail: [email protected]
Web: www.underctrl.de
Distributed by: EMDC ®
⏩ EMDC Network: https://emdcnetwork.com
(YouTube MCN, Digitalni marketing i all-round usluge)
🔊 EMDC Music: https://emdcmusic.com
(Platforma za distribuciju muzike)
🎶 EMDC Publishing: https://emdcpublishing.com
(Licence za covere i zastupanje autorskih prava)
📷 Instagram: https://instagram.com/emdc_network
Originalni nazivi pesama, linkovi do pesama i autori:
1: MC STOJAN - LA MIAMI
Music: Nek Music , MC Stojan
Text : MC Stojan , Jovan Jankovic , Vuksan Bilanovic
https://www.youtube.com/watch?v=nuw6TLOEm7Q
2: EDITA - ŽIVOTINJE
Muzika: Bojan Vasic
Tekst: Aleksandar Tomic
https://www.youtube.com/watch?v=YSPWgg7wzEc
3: SAŠA KOVACEVIC - LAPSUS
Muzika: Mihalis Hatzgiannis
Tekst: Miloš Roganovic
https://www.youtube.com/watch?v=KIa54IniRvQ
4: JALA BRAT X BUBA CORELLI X SENIDAH - KAMIKAZA
Muzika i tekst: Jala Brat & Buba Corelli
https://www.youtube.com/watch?v=oZQQhOyqeTQ
5: TOŠE PROESKI - CIJA SI
Muzika i tekst: L. Vukomanovic
https://www.youtube.com/watch?v=LkJghgD8tPA
6: ANA NIKOLIC FEAT. RASTA - KONKRETNO
Muzika: Stefan Djuric Rasta, Slobodan Veljkovic Coby
Tekst: Sefan Djuric Rasta, Antonije Stojiljkovic Toni
https://www.youtube.com/watch?v=CEU1hm1iyi0
7: MAGLA BAND - SAMO SE NOCAS POJAVI
Muzika: Vasilis Dimas
Tekst: Jelena Trifunovic
https://www.youtube.com/watch?v=jSlQS1WpOGI
8: BUBA CORELLI FT. NAIDA BEŠLAGIC - PREMIJA
Muzika i tekst: Jala Brat & Buba Corelli
https://www.youtube.com/watch?v=cfQfkeeAvnc
9: CVIJA & RELJA FEAT. COBY - CRNI SIN
Muzika i tekst: Coby / Relja / Cvija
https://www.youtube.com/watch?v=KF-9RpwhHco
10: MAYA BEROVIC FEAT. BUBA CORELLI - PRAVO VREME
Muzika i tekst: Jala Brat, Buba Corelli
https://www.youtube.com/watch?v=TVuipQx5zYY
11: RELJA X COBY X STOJA - SAMO JAKO
Muzika: Veljkovic Slobodan Coby, Relja Popovic
Tekst: Veljkovic Slobodan Coby, Ðorde Ðordevic
https://www.youtube.com/watch?v=95zxduB-WrI
12: TRIBAL BAND - DO MENE JE
Muzika i tekst: Bane Opacic
https://www.youtube.com/watch?v=76vUQ79j8MY
13: JOCE PANOV - NOCAS KUPUJEM ILUZIJE
Muzika: Miro Buljan
Tekst: Nenad Nincevic
https://www.youtube.com/watch?v=ACS558Ug7v4
14: TANJA SAVIC X CORONA - LAGA LAGA
Muzika: Corona, Filip Mladenovic - One Music
Tekst: Corona, Filip Mladenovic - One Music
https://www.youtube.com/watch?v=eO-q9NPXks4
#AlexandraMatrix #Mashup #LagaLaga #TanjaSavic #Corona #JocePanov
ALEXANDRA on Instagram:
https://www.instagram.com/alexandra.matrix/
ALEXANDRA ON TIK TOK:
https://www.tiktok.com/@alexandra.matrix
✔ Social Media:
https://emdc.yt/alexandramatrix
✔ Stream & Download:
https://emdc.yt/lagalaga
MANAGER: +38765598621 – RAJKO JOVANIC
Alexandra & Matrix Band Official Youtube Channel
Recording, Mix & Master: Filip Mladenovic - One Music
Video by: TOXIC
Zabranjeno svako kopiranje video i/ili audio snimaka i postavljanje na druge kanale!
Marketing:
UNDER CONTROL
Marketing Management
BLKN +387 65 598 621
EU +49 176 432696 01
Mail: [email protected]
Web: www.underctrl.de
Distributed by: EMDC ®
⏩ EMDC Network: https://emdcnetwork.com
(YouTube MCN, Digitalni marketing i all-round usluge)
🔊 EMDC Music: https://emdcmusic.com
(Platforma za distribuciju muzike)
🎶 EMDC Publishing: https://emdcpublishing.com
(Licence za covere i zastupanje autorskih prava)
📷 Instagram: https://instagram.com/emdc_network
Originalni nazivi pesama, linkovi do pesama i autori:
1: MC STOJAN - LA MIAMI
Music: Nek Music , MC Stojan
Text : MC Stojan , Jovan Jankovic , Vuksan Bilanovic
https://www.youtube.com/watch?v=nuw6TLOEm7Q
2: EDITA - ŽIVOTINJE
Muzika: Bojan Vasic
Tekst: Aleksandar Tomic
https://www.youtube.com/watch?v=YSPWgg7wzEc
3: SAŠA KOVACEVIC - LAPSUS
Muzika: Mihalis Hatzgiannis
Tekst: Miloš Roganovic
https://www.youtube.com/watch?v=KIa54IniRvQ
4: JALA BRAT X BUBA CORELLI X SENIDAH - KAMIKAZA
Muzika i tekst: Jala Brat & Buba Corelli
https://www.youtube.com/watch?v=oZQQhOyqeTQ
5: TOŠE PROESKI - CIJA SI
Muzika i tekst: L. Vukomanovic
https://www.youtube.com/watch?v=LkJghgD8tPA
6: ANA NIKOLIC FEAT. RASTA - KONKRETNO
Muzika: Stefan Djuric Rasta, Slobodan Veljkovic Coby
Tekst: Sefan Djuric Rasta, Antonije Stojiljkovic Toni
https://www.youtube.com/watch?v=CEU1hm1iyi0
7: MAGLA BAND - SAMO SE NOCAS POJAVI
Muzika: Vasilis Dimas
Tekst: Jelena Trifunovic
https://www.youtube.com/watch?v=jSlQS1WpOGI
8: BUBA CORELLI FT. NAIDA BEŠLAGIC - PREMIJA
Muzika i tekst: Jala Brat & Buba Corelli
https://www.youtube.com/watch?v=cfQfkeeAvnc
9: CVIJA & RELJA FEAT. COBY - CRNI SIN
Muzika i tekst: Coby / Relja / Cvija
https://www.youtube.com/watch?v=KF-9RpwhHco
10: MAYA BEROVIC FEAT. BUBA CORELLI - PRAVO VREME
Muzika i tekst: Jala Brat, Buba Corelli
https://www.youtube.com/watch?v=TVuipQx5zYY
11: RELJA X COBY X STOJA - SAMO JAKO
Muzika: Veljkovic Slobodan Coby, Relja Popovic
Tekst: Veljkovic Slobodan Coby, Ðorde Ðordevic
https://www.youtube.com/watch?v=95zxduB-WrI
12: TRIBAL BAND - DO MENE JE
Muzika i tekst: Bane Opacic
https://www.youtube.com/watch?v=76vUQ79j8MY
13: JOCE PANOV - NOCAS KUPUJEM ILUZIJE
Muzika: Miro Buljan
Tekst: Nenad Nincevic
https://www.youtube.com/watch?v=ACS558Ug7v4
14: TANJA SAVIC X CORONA - LAGA LAGA
Muzika: Corona, Filip Mladenovic - One Music
Tekst: Corona, Filip Mladenovic - One Music
https://www.youtube.com/watch?v=eO-q9NPXks4
#AlexandraMatrix #Mashup #LagaLaga #TanjaSavic #Corona #JocePanov
Goal.
Explaining basic concepts of (a classical course in) algebra in an intuitive way.
This time.
What are...matrix groups? Or: The most important groups?!
...
Goal.
Explaining basic concepts of (a classical course in) algebra in an intuitive way.
This time.
What are...matrix groups? Or: The most important groups?!
Disclaimer.
Nobody is perfect, and I might have said something silly. If there is any doubt, then please check the references.
Slides.
http://www.dtubbenhauer.com/youtube.html
Material used.
https://en.wikipedia.org/wiki/General_linear_group
https://en.wikipedia.org/wiki/Linear_group
https://en.wikipedia.org/wiki/Automorphism_group
https://en.wikipedia.org/wiki/Special_linear_group
Multiplication table of SL2(F3).
https://en.wikipedia.org/wiki/Special_linear_group#/media/File:SL(2,3);_Cayley_table.svg
Periodic table.
https://irandrus.files.wordpress.com/2012/06/periodic-table-of-groups.pdf
Mathematica.
https://demonstrations.wolfram.com/GL2PAndGL33ActingOnPoints/
#algebra
#galoistheory
#mathematics
Goal.
Explaining basic concepts of (a classical course in) algebra in an intuitive way.
This time.
What are...matrix groups? Or: The most important groups?!
Disclaimer.
Nobody is perfect, and I might have said something silly. If there is any doubt, then please check the references.
Slides.
http://www.dtubbenhauer.com/youtube.html
Material used.
https://en.wikipedia.org/wiki/General_linear_group
https://en.wikipedia.org/wiki/Linear_group
https://en.wikipedia.org/wiki/Automorphism_group
https://en.wikipedia.org/wiki/Special_linear_group
Multiplication table of SL2(F3).
https://en.wikipedia.org/wiki/Special_linear_group#/media/File:SL(2,3);_Cayley_table.svg
Periodic table.
https://irandrus.files.wordpress.com/2012/06/periodic-table-of-groups.pdf
Mathematica.
https://demonstrations.wolfram.com/GL2PAndGL33ActingOnPoints/
#algebra
#galoistheory
#mathematics
Collection of all non-singular matrices, whose elements are taken from a field.
#generallineargroup
#matrixgroup
#groupofmatrices
#grouptheory
#abstractalgebra...
Collection of all non-singular matrices, whose elements are taken from a field.
#generallineargroup
#matrixgroup
#groupofmatrices
#grouptheory
#abstractalgebra
Collection of all non-singular matrices, whose elements are taken from a field.
#generallineargroup
#matrixgroup
#groupofmatrices
#grouptheory
#abstractalgebra
In this video, we survey the classical matrix groups, namely the general linear group, the special linear group, the orthogonal group, the special orthogonal gr...
In this video, we survey the classical matrix groups, namely the general linear group, the special linear group, the orthogonal group, the special orthogonal group, the unitary group, the special unitary group, and the sympletic group. We briefly discuss their importance to geometry, simple groups, and physical science.
This is lecture 35 (part 1/3) of the lecture series offered by Dr. Andrew Misseldine for the course Math 4220 - Abstract Algebra I at Southern Utah University. A transcript of this lecture can be found at Dr. Misseldine's website or through his Google Drive at:
https://drive.google.com/file/d/1V9Pt3zBqYWkccHWVvPqPocwhyWBorp72/view
This lecture is based upon Section 12.1 of Abstract Algebra: Theory and Applications (http://abstract.ups.edu/) by Tom Judson. Please post any questions you might have below in the comment field and Dr. Misseldine (or other commenters) can answer them for you. Please also subscribe for further updates.
In this video, we survey the classical matrix groups, namely the general linear group, the special linear group, the orthogonal group, the special orthogonal group, the unitary group, the special unitary group, and the sympletic group. We briefly discuss their importance to geometry, simple groups, and physical science.
This is lecture 35 (part 1/3) of the lecture series offered by Dr. Andrew Misseldine for the course Math 4220 - Abstract Algebra I at Southern Utah University. A transcript of this lecture can be found at Dr. Misseldine's website or through his Google Drive at:
https://drive.google.com/file/d/1V9Pt3zBqYWkccHWVvPqPocwhyWBorp72/view
This lecture is based upon Section 12.1 of Abstract Algebra: Theory and Applications (http://abstract.ups.edu/) by Tom Judson. Please post any questions you might have below in the comment field and Dr. Misseldine (or other commenters) can answer them for you. Please also subscribe for further updates.
Matrices are a great example of infinite, nonabelian groups. Here we introduce matrix groups with an emphasis on the general linear group and special linear group. The general linear group is written as GLn(F), where F is the field used for the matrix elements. The most common examples are GLn(R) and GLn(C). Similarly, the special linear group is written as SLn.
Be sure to subscribe so you don't miss new lessons from Socratica:
http://bit.ly/1ixuu9W
♦♦♦♦♦♦♦♦♦♦
We recommend the following textbooks:
Dummit & Foote, Abstract Algebra 3rd Edition
http://amzn.to/2oOBd5S
Milne, Algebra Course Notes (available free online)
http://www.jmilne.org/math/CourseNotes/index.html
♦♦♦♦♦♦♦♦♦♦
Ways to support our channel:
► Join our Patreon : https://www.patreon.com/socratica
► Make a one-time PayPal donation: https://www.paypal.me/socratica
► We also accept Bitcoin @ 1EttYyGwJmpy9bLY2UcmEqMJuBfaZ1HdG9
Thank you!
♦♦♦♦♦♦♦♦♦♦
Connect with us!
Facebook: https://www.facebook.com/SocraticaStudios/
Instagram: https://www.instagram.com/SocraticaStudios/
Twitter: https://twitter.com/Socratica
♦♦♦♦♦♦♦♦♦♦
Teaching Assistant: Liliana de Castro
Written & Directed by Michael Harrison
Produced by Kimberly Hatch Harrison
♦♦♦♦♦♦♦♦♦♦
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys
The General Linear Group, The Special Linear Group, The Group C^n with Componentwise Multiplication
It was a long time after I started mixing audio that I really learned what the difference between a group, an aux, and a matrix was. They all process and route audio, but in different ways, so it's easy to get them confused and not know which one to use for which application. In this video, I'll teach you the difference between them and give you practical applications for each one. Hope this helps!
Also, don't forget to get your FREE "7 Step Mix" download!
https://www.themixingprocess.com/
- Schuyler
In this lecture we are taking set of matrices as a set and with this set we are going to show it is an abelian group under matrix addition. Firstly we will take matrix of order 2 and we will show that this collection of matrices satisfies all the properties of a group with the operation of matrix addition .After this we will take a general case in which we will consider a set of all matrices of any dimension and we prove it that this set is also an abelian group under matrix addition.
If anyone has any doubt regarding this lecture do mention it in the comment section.
Keep connected with Theta Classes to study various topics of higher mathematics.
ALEXANDRA on Instagram:
https://www.instagram.com/alexandra.matrix/
ALEXANDRA ON TIK TOK:
https://www.tiktok.com/@alexandra.matrix
✔ Social Media:
https://emdc.yt/alexandramatrix
✔ Stream & Download:
https://emdc.yt/lagalaga
MANAGER: +38765598621 – RAJKO JOVANIC
Alexandra & Matrix Band Official Youtube Channel
Recording, Mix & Master: Filip Mladenovic - One Music
Video by: TOXIC
Zabranjeno svako kopiranje video i/ili audio snimaka i postavljanje na druge kanale!
Marketing:
UNDER CONTROL
Marketing Management
BLKN +387 65 598 621
EU +49 176 432696 01
Mail: [email protected]
Web: www.underctrl.de
Distributed by: EMDC ®
⏩ EMDC Network: https://emdcnetwork.com
(YouTube MCN, Digitalni marketing i all-round usluge)
🔊 EMDC Music: https://emdcmusic.com
(Platforma za distribuciju muzike)
🎶 EMDC Publishing: https://emdcpublishing.com
(Licence za covere i zastupanje autorskih prava)
📷 Instagram: https://instagram.com/emdc_network
Originalni nazivi pesama, linkovi do pesama i autori:
1: MC STOJAN - LA MIAMI
Music: Nek Music , MC Stojan
Text : MC Stojan , Jovan Jankovic , Vuksan Bilanovic
https://www.youtube.com/watch?v=nuw6TLOEm7Q
2: EDITA - ŽIVOTINJE
Muzika: Bojan Vasic
Tekst: Aleksandar Tomic
https://www.youtube.com/watch?v=YSPWgg7wzEc
3: SAŠA KOVACEVIC - LAPSUS
Muzika: Mihalis Hatzgiannis
Tekst: Miloš Roganovic
https://www.youtube.com/watch?v=KIa54IniRvQ
4: JALA BRAT X BUBA CORELLI X SENIDAH - KAMIKAZA
Muzika i tekst: Jala Brat & Buba Corelli
https://www.youtube.com/watch?v=oZQQhOyqeTQ
5: TOŠE PROESKI - CIJA SI
Muzika i tekst: L. Vukomanovic
https://www.youtube.com/watch?v=LkJghgD8tPA
6: ANA NIKOLIC FEAT. RASTA - KONKRETNO
Muzika: Stefan Djuric Rasta, Slobodan Veljkovic Coby
Tekst: Sefan Djuric Rasta, Antonije Stojiljkovic Toni
https://www.youtube.com/watch?v=CEU1hm1iyi0
7: MAGLA BAND - SAMO SE NOCAS POJAVI
Muzika: Vasilis Dimas
Tekst: Jelena Trifunovic
https://www.youtube.com/watch?v=jSlQS1WpOGI
8: BUBA CORELLI FT. NAIDA BEŠLAGIC - PREMIJA
Muzika i tekst: Jala Brat & Buba Corelli
https://www.youtube.com/watch?v=cfQfkeeAvnc
9: CVIJA & RELJA FEAT. COBY - CRNI SIN
Muzika i tekst: Coby / Relja / Cvija
https://www.youtube.com/watch?v=KF-9RpwhHco
10: MAYA BEROVIC FEAT. BUBA CORELLI - PRAVO VREME
Muzika i tekst: Jala Brat, Buba Corelli
https://www.youtube.com/watch?v=TVuipQx5zYY
11: RELJA X COBY X STOJA - SAMO JAKO
Muzika: Veljkovic Slobodan Coby, Relja Popovic
Tekst: Veljkovic Slobodan Coby, Ðorde Ðordevic
https://www.youtube.com/watch?v=95zxduB-WrI
12: TRIBAL BAND - DO MENE JE
Muzika i tekst: Bane Opacic
https://www.youtube.com/watch?v=76vUQ79j8MY
13: JOCE PANOV - NOCAS KUPUJEM ILUZIJE
Muzika: Miro Buljan
Tekst: Nenad Nincevic
https://www.youtube.com/watch?v=ACS558Ug7v4
14: TANJA SAVIC X CORONA - LAGA LAGA
Muzika: Corona, Filip Mladenovic - One Music
Tekst: Corona, Filip Mladenovic - One Music
https://www.youtube.com/watch?v=eO-q9NPXks4
#AlexandraMatrix #Mashup #LagaLaga #TanjaSavic #Corona #JocePanov
Goal.
Explaining basic concepts of (a classical course in) algebra in an intuitive way.
This time.
What are...matrix groups? Or: The most important groups?!
Disclaimer.
Nobody is perfect, and I might have said something silly. If there is any doubt, then please check the references.
Slides.
http://www.dtubbenhauer.com/youtube.html
Material used.
https://en.wikipedia.org/wiki/General_linear_group
https://en.wikipedia.org/wiki/Linear_group
https://en.wikipedia.org/wiki/Automorphism_group
https://en.wikipedia.org/wiki/Special_linear_group
Multiplication table of SL2(F3).
https://en.wikipedia.org/wiki/Special_linear_group#/media/File:SL(2,3);_Cayley_table.svg
Periodic table.
https://irandrus.files.wordpress.com/2012/06/periodic-table-of-groups.pdf
Mathematica.
https://demonstrations.wolfram.com/GL2PAndGL33ActingOnPoints/
#algebra
#galoistheory
#mathematics
Collection of all non-singular matrices, whose elements are taken from a field.
#generallineargroup
#matrixgroup
#groupofmatrices
#grouptheory
#abstractalgebra
In this video, we survey the classical matrix groups, namely the general linear group, the special linear group, the orthogonal group, the special orthogonal group, the unitary group, the special unitary group, and the sympletic group. We briefly discuss their importance to geometry, simple groups, and physical science.
This is lecture 35 (part 1/3) of the lecture series offered by Dr. Andrew Misseldine for the course Math 4220 - Abstract Algebra I at Southern Utah University. A transcript of this lecture can be found at Dr. Misseldine's website or through his Google Drive at:
https://drive.google.com/file/d/1V9Pt3zBqYWkccHWVvPqPocwhyWBorp72/view
This lecture is based upon Section 12.1 of Abstract Algebra: Theory and Applications (http://abstract.ups.edu/) by Tom Judson. Please post any questions you might have below in the comment field and Dr. Misseldine (or other commenters) can answer them for you. Please also subscribe for further updates.
These elements are "special" in that they fall on a subvariety of the general linear group – they satisfy a polynomial equation (since the determinant is polynomial in the entries).
Geometric interpretation
The special linear group SL(n, R) can be characterized as the group of volume and orientation preserving linear transformations of Rn; this corresponds to the interpretation of the determinant as measuring change in volume and orientation.
Lie subgroup
When F is R or C, SL(n, F) is a Lie subgroup of GL(n, F) of dimension n2 − 1. The Lie algebra of SL(n, F) consists of all n × n matrices over F with vanishing trace. The Lie bracket is given by the commutator.