Matrix Groups: crash course 2015 by James Cook

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source: James Cook     2015年8月11日
Matrix Groups: crash course 2015
Here I give a series of little talks that walk you through my notes from reading Tapp's "Matrix Groups for Undergraduates". We see a good amount of detail about the complex linear matrices or quaternionic linear matrices which are special matrices of real numbers which encode the multiplication of complex or quaternionic matrices. Then, the later part of the talks outlines the rudiments of Lie Theory of Groups and Algebras in the context of matrices. Here probably too much detail is missing, so don't be discouraged if it's hard to follow. Finally we do some sight-seeing about the classification theory of compact connected Lie groups and the theory of maximal tori.
I assume the audience has some experience with manifold theory or differential geometry and a willingness to learn some group theory on the fly. Almost everything I say in these talks is also found directly in Tapp where you will also find further discussion and much more depth. Ideally, these videos might convince you to study further.

Matrix Groups: Part 1 13:42 In this talk we cover pages 1 to 4 of my notes where the K-notation for K=R,C,H is explained and the general linear group of nxn matrices over K is defined. We also begin to explain mapping which embeds nxn complex matrices in 2nx2n real matrices.
Part 2 20:16
Part 3 15:26
Part 4 13:47
Part 5 16:52
Part 6 13:34
Part 7 13:47
Part 8 5:18
Part 9 21:28
Part 10 7:09
Part 11 9:12
Part 12 7:54
Part 13 25:32
Part 14 11:01

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