A First Course In Linear Algebra / Minking Eie, Shou-Te Chang.

TABLE OF CONTENTS
Intro; Contents; Preface; Notation; About the Authors; 1 Vector Spaces; 1.1 A few words on sets and logics; 1.2 What constitutes a vector space?; 1.3 Subspaces; 1.4 How to solve a system of linear equations; Review Exercises for Chapter 1; 2 Bases and Dimension; 2.1 Observations in R2 and in R3; 2.2 Linear combinations; 2.3 Linear dependence and independence; 2.4 Bases and dimension; 2.5 Applications; 2.6 Further examples; Review Exercises for Chapter 2; 3 Linear Transformations and Matrices; 3.1 Linear transformations; 3.2 Isomorphisms; 3.3 Range and null space. 3.4 Matrices and linear transformations3.5 Composites and inverses; Review Exercises for Chapter 3; 4 Elementary Matrix Operations; 4.1 Elementary matrix operations; 4.2 The rank and the inverse of a matrix; 4.3 A description of determinants; 4.4 Applications in linear programming; Review Exercises for Chapter 4; 5 Diagonalization; 5.1 Base change; 5.2 Eigenvalues and eigenvectors; 5.3 Diagonalizability; 5.4 Powers of a square matrix; 5.5 Differential equations; Review Exercises for Chapter 5; 6 Canonical Forms; 6.1 Cayley-Hamilton theorem; 6.2 Jordan canonical forms. 6.3 How to find Jordan canonical formsReview Exercises for Chapter 6; 7 Inner Product Spaces; 7.1 Inner product spaces; 7.2 Norm and angle; 7.3 The spectral theorem; 7.4 Applications of the spectral theorem; 7.5 The method of least squares; 7.6 The L2-approximation of a continuous function; Review Exercises for Chapter 7; Index