Rigorous, self-contained introduction at undergraduate level covers vector spaces and linear transformations, linear equations and determinants, characteristic roots. Includes 16 sets of true-false quizzes and exercises with worked-out solutions a complete theory of permutations and much more.

Preface
Chapter 1: Vector Spaces and Linear Transformations
1. Vector Spaces
2. Linear transformations
3. Inner product
4. Matrix representations
5. Inverses
Chapter 2: Linear Equations and Determinants
1. Rank of a matrix
2. Operations on matrices
3. Linear equations
4. Permutations
5. Introduction to determinants
6. Properties of determinants
Chapter 3: Characteristic Roots
1. Characteristic roots and characteristic vectors
2. Schur's theorem
3. Normal matrices
4. Hermitian matrices
5. Matrix inequalities
Answers and Solutions
Index

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