By Steven H. Weintraub
Linear algebra occupies a critical position in glossy arithmetic. This e-book presents 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 number of themes is ruled not just for his or her significance in linear algebra itself, but additionally for his or her purposes 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 material will make this e-book a invaluable reference for mathematicians all through their specialist lives.
Topics handled during this e-book comprise: vector areas and linear adjustments; size counting and functions; illustration of linear ameliorations by way of matrices; duality; determinants and their makes use of; rational and particularly Jordan canonical shape; bilinear varieties; internal product areas; general linear modifications and the spectral theorem; and an creation to matrix teams as Lie groups.
The ebook treats vector areas in complete generality, notwithstanding 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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