Matrix Groups (Abstract Algebra)

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.

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We recommend the following textbooks:
Dummit & Foote, Abstract Algebra 3rd Edition

Milne, Algebra Course Notes (available free online)

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Teaching​ ​Assistant:​ ​​ ​Liliana​ ​de​ ​Castro
Written​ ​&​ ​Directed​ ​by​ ​Michael​ ​Harrison
Produced​ ​by​ ​Kimberly​ ​Hatch​ ​Harrison

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[thcoura]

14 videos in a row.. I shall continue..

[algonte]

Never expected to become a enthusiastic of groups :-)

[zahramohammadi]

The explanation was perfect. Thank you

[prince-d]

Absolutely distinguish from others.
It's preserving joy of mathematics.

[conradgarcia]

Thank you so much for these videos. You're able to break it down into nice and orderly chunks which is accessible even to laymen. This is a good refresher course for higher mathematics. Please make more!

[Algebrodadio]

Are you going to talk about representation theory? Or Lie groups and Lie algebras?

[NKernytskyy]

Dear Google, please adjust YouTube algorithm to favor this amazingly great channel and monetize it lavishly. Thank you.

[cameronspalding]

For a field F and integer n: if we denote GLn(F) is the group of invertible matrices under multiplication with entries in F and denote SLn(F) as the subset of GLn(F) where each element has a determinant 1: then SLn(F) is a normal subgroup of GLn(F)

[PunmasterSTP]

It's a new day where I am, and I'm already starting another binge-watch. I can't tell you how amazing your videos are, and how much I wish that I had come across them years ago...

[meghanilsinha]

your way of explaining is too good
can you add some videos on.cryptography and number theory??

[muhammadafaan]

Kindly upload more examples related to cyclic group normal group cosets etc, as soon as possible

[johnstaf]

Thank you ma'am. This is wonderful!

[ajymediadaawah]

Please what is the name of the music u used in the video
The name plss or something similar

[davidjohansson]

Is it possible to solve geometric problems in grouptheory using matrices? For example reflections + rotations of a triangle etc.? Or how do you rigurously prove that you have got back to the identity of the triangle for example.

[derciferreira]

can we multiply  matrix groups of different order? if so, how is it made? by the way excellent videos!

[milos_radovanovic]

Could you plies, for easy reference, add group notations to the description of videos talking about or mentioning particular groups like Dn, Sn, GLn ?

[masterstghm]

Thank you for these videos! I wish my professor was this coherent!

[CauchemarKnight]

a vídeo of the isomorphism theorems... :D please

[mathematicslectures]

Can you please tell me that if we are given a set of real valued function whose domain and range is real number then will composition of function be group or not please help

[Polyviani]

Why is complex under addition only is infinite? What is an example to non Abel own finite? You gotta use more examples and not just terms