Introduction to Linear Algebra

Title Contents Preface 1. Introduction to Linearity 2. Sets and Functions 1 / Sets 2 / Functions 3 / Counting 4 / Induction 3. Vector Spaces 1 / Definitions and Examples 2 / Products and Powers of Vector Spaces 3 / Vector Subspaces, Subspace Sums, and Subspace Products 4 / Hyperplanes and Quotients of Vector Spaces 5 / Linear Dependence and Independence, Bases and Dimension 4. Linear Transformations 1 / Basic Definitions and Results 2 / Construction of Linear Transformations 3 / Duality in Vector Spaces 4 / Linear Transformations and Matrices 5. Linear Equations and Determinants 1 / Introduction and Qualitative Analysis 2 / Elimination of Variables or Row Reduction 3 / Determinants 6. Inner Product Spaces 1 / Angles and Distances in R^2 and in C 2 / Bilinear Forms, Conjugate-Bilinear Forms, and Inner Products 3 / Inner Product Spaces 7. Canonical Forms 1 / The Effect of a Basis Change 2 / Invariant Subspaces 3 / Triangular Form 4 / Polynomials and Invariant Subspaces 5 / Diagonal Forms -- the Spectral Theorem Index Major Symbols