Groups, Matrices, and Vector Spaces A Group Theoretic Approach to Linear Algebra /

• Main Author: Carrell, James B. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York : Imprint: Springer, 2017.
• Subjects: Mathematics.; Algebraic geometry.; Commutative algebra.; Commutative rings.; Group theory.; Matrix theory.; Algebra.; Commutative Rings and Algebras.; Linear and Multilinear Algebras, Matrix Theory.; Group Theory and Generalizations.; Algebraic Geometry.

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...

Table of Contents:

• 1. Preliminaries
• 2. Groups and Fields: The Two Fundamental Notions of Algebra
• 3. Vector Spaces
• 4. Linear Mappings
• 5. Eigentheory
• 6. Unitary Diagonalization and Quadratic Forms
• 7. The Structure Theory of Linear Mappings
• 8. Theorems on Group Theory
• 9. Linear Algebraic Groups: An Introduction
• Bibliography
• Index.