# A Guide to Advanced Linear Algebra by Steven H. Weintraub

By Steven H. Weintraub

Linear algebra occupies a vital position in glossy arithmetic. This e-book offers a rigorous and thorough improvement of linear algebra at a complicated point, and is directed at graduate scholars mathematicians. It ways linear algebra from an algebraic viewpoint, yet its collection of themes is ruled not just for his or her value in linear algebra itself, but additionally for his or her functions all through arithmetic. scholars in algebra, research, and topology will locate a lot of curiosity and use to them, and the cautious therapy and breadth of subject material will make this e-book a worthwhile reference for mathematicians all through their specialist lives.

Topics taken care of during this booklet contain: vector areas and linear variations; size counting and functions; illustration of linear adjustments by means of matrices; duality; determinants and their makes use of; rational and particularly Jordan canonical shape; bilinear kinds; internal product areas; common linear changes and the spectral theorem; and an advent to matrix teams as Lie groups.

The booklet treats vector areas in complete generality, although it concentrates at the finite dimensional case. additionally, it treats vector areas over arbitrary fields, specializing to algebraically closed fields or to the fields of genuine and complicated numbers as necessary.

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