Groups, Matrices, and Vector Spaces: A Group Theoretic Approach to Linear Algebra 1st ed. 2017 Edition

Ebook Details

Authors

James B. Carrell

Year 2017
Pages 410
Publisher Springer
Language en
ISBN 9780387794273
File Size 3.01 MB
File Format PDF
Download Counter 425
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Ebook Description

This unique text provides a geometric approach to group theory and linear algebra, bringing to light the interesting ways in which these subjects interact. Requiring few prerequisites beyond understanding the notion of a proof, the text aims to give students a strong foundation in both geometry and algebra. Starting with preliminaries (relations, elementary combinatorics, and induction), the book then proceeds to the core topics: the elements of the theory of groups and fields (Lagrange's Theorem, cosets, the complex numbers and the prime fields), matrix theory and matrix groups, determinants, vector spaces, linear mappings, eigentheory and diagonalization, Jordan decomposition and normal form, normal matrices, and quadratic forms. The final two chapters consist of a more intensive look at group theory, emphasizing orbit stabilizer methods, and an introduction to linear algebraic groups, which enriches the notion of a matrix group.