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After studying general a linear algebra course, how would an advanced linear algebra course differ from the general course?

And would an advanced linear algebra course be taught in graduate schools?

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    More advance linear algebra would probably be areas of algebra that uses modules and linear algebra. Maybe stuff like Tensor Products, Projective injective flat modules, homological algebra, representation theory, Galois Theory, and Algebraic Number Theory.2012-08-23
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    Like the guys above said, you can think of Linear Algebra is a sort of "sophisticated, ideal form" of an algebraic structure. The study of L.A. focuses on vector spaces. In algebra, you can relax certain axioms of vector spaces and generalize groups, rings, and fields (among other things...). Conversely, you can start with basic group/ring theory and build up by adding axioms to form an algebraic vector space.2012-08-23
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    Instead of speculations, how about someone citing an actual "advanced linear algebra" textbook?2012-08-23
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    Steve Roman, Advanced Linear Algebra, Springer, 2005; Bruce Cooperstein, Advanced Linear Algebra, CRC Press, 2010; Steven H Weintraub, A Guide to Advanced Linear Algebra, MAA 2011; O'Meara, Clark, and Vinsonhaler, Advanced Topics in Linear Algebra, Oxford, 2011; Dianat and Saber, Advanced Linear Algebra for Engineers with Matlab, Taylor and Francis, 2009.2012-08-24
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    Adding to other comments: Linear models and multivariate analysis in statistics can be seen as a sort of "advanced linear algebra". I have learnt a lot of linear algebra stuff from appendices to such books!2012-09-22

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