Table of Contents

1. Matrices 1.1 Definitions and Elementary Properties 1.2 Matrix Multiplication 1.3 Diagonal Matrices 1.4 Special Real Matrices 1.5 Special Complex Matrices 2. Inverse and Systems of Matrices 2.1 Determinants 2.2 Inverse of a Matrix 2.3 Systems of Matrices 2.4 Rank of a Matrix 2.5 Systems of Linear Equations 3. Transformation of the Plane 3.1 Mappings 3.2 Rotations 3.3 Reflections, Dilations, and Magnifications 3.4 Other Transformations 3.5 Linear Homogeneous Transformations 3.6 Orthogonal Matrices 3.7 Translations 3.8 Rigid Motion Transformations 4. Eigenvalues and Eigenvectors 4.1 Characteristic Functions 4.2 A Geometric Interpretaion of Eigenvectors 4.3 Some Theorems 4.4 Diagonalization of Matrices 4.5 The Hamilton-Cayley Theorem 4.6 Quadratic Forms 4.7 Classification of the Conics 4.8 Invariants for Conics Bibliography; Answers to Odd-Numbered Exercises; Index