Book:A.O. Morris/Linear Algebra: An Introduction

Subject Matter

 * Linear Algebra

Contents

 * PREFACE


 * CHAPTER 1 - LINEAR EQUATIONS AND MATRICES
 * 1.1 Introduction
 * 1.2 Elementary Row Operations on Matrices
 * 1.3 Application to Linear Equations
 * 1.4 Matrix Algebra
 * 1.5 Special Types of Matrices
 * 1. Identity Matrix
 * 2. Diagonal Matrix
 * 3. Inverse Matrix
 * 4. Transpose of a Matrix
 * 5. Symmetric, Skew-symmetric and Orthogonal Matrices
 * 1.6 Elementary Matrices
 * 1.7 Elementary Column Operations and Equivalent Matrices


 * CHAPTER 2 - DETERMINANTS
 * 2.1 $2 \times 2$ and $3 \times 3$ Determinants
 * 2.2 $n \times n$ Determinants
 * 2.3 Further Properties of Determinants
 * 2.4 The Inverse of a Matrix


 * CHAPTER 3 - VECTOR SPACES
 * 3.1 Introduction
 * 3.2 Definition and Examples of Vector Spaces
 * 3.3 Subspaces
 * 3.4 Linear Independence, Basis and Dimension


 * CHAPTER 4 - LINEAR TRANSFORMATIONS ON VECTOR SPACES
 * 4.1 Linear Transformations
 * 4.2 The Matrix of a Linear Transformation
 * 4.3 Change of Basis
 * 4.4 The Kernel and Image of a Linear Transformation
 * 4.5 $K$-Isomorphisms and Non-singular Linear Transformations
 * 4.6 Applications to linear Equations and the Rank of Matrices


 * CHAPTER 5 - INNER PRODUCT SPACES
 * 5.1 Introduction and Three-Dimensional Geometry
 * 5.2 Euclidean and Unitary Spaces
 * 5.3 Orthogonal Vectors
 * 5.4 Application to the Rank of a Matrix


 * CHAPTER 6 - DIAGONALIZATION OF MATRICES AND LINEAR TRANSFORMATIONS
 * 6.1 Introduction
 * 6.2 Eigenvalues and Eigenvectors
 * 6.3 Diagonalization of Matrices
 * 6.4 The Minimum Polynomial of a Matrix and the Cayley-Hamilton Theorem
 * 6.5 The Diagonalization of Symmetric Matrices
 * 6.6 Quadratic Forms


 * APPENDIX 1 CONIC SECTIONS


 * APPENDIX 2 QUADRATIC SURFACES


 * SOLUTIONS TO EXERCISES


 * INDEX