ABSTRACT

Designed for advanced undergraduate and beginning graduate students in linear or abstract algebra, Advanced Linear Algebra covers theoretical aspects of the subject, along with examples, computations, and proofs. It explores a variety of advanced topics in linear algebra that highlight the rich interconnections of the subject to geometry, algebra,

part 1|2 pages

Part I: Background on Algebraic Structures

chapter 1|20 pages

Overview of Algebraic Systems

chapter 2|12 pages

Permutations

chapter 3|36 pages

Polynomials

part 2|2 pages

Part II: Matrices

chapter 4|28 pages

Basic Matrix Operations

chapter 5|30 pages

Determinants via Calculations

chapter 6|36 pages

Concrete vs. Abstract Linear Algebra

part 3|2 pages

Part III: Matrices with Special Structure

chapter 8|24 pages

Jordan Canonical Forms

chapter 9|26 pages

Matrix Factorizations

part 4|2 pages

Part IV: The Interplay of Geometry and Linear Algebra

chapter 11|36 pages

Affine Geometry and Convexity

chapter 12|26 pages

Ruler and Compass Constructions

chapter 13|24 pages

Dual Spaces and Bilinear Forms

chapter 14|36 pages

Metric Spaces and Hilbert Spaces

part 5|2 pages

Part V: Modules, Independence, and Classification Theorems

part 6|2 pages

Part VI: Universal Mapping Properties and Multilinear Algebra

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