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

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.

Applications involving symm

Emphasizes the interplay between algebra and geometry

Accessible to advanced undergraduates/graduate students, in a variety of subject areas, including mathematics, physics, engineering, and computer science

Useful reference material for mathematicians and professionals

Contains numerous practice problems at the end of each section

Includes supplementary material: sn.pub/extras