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

## A.O. Morris: Linear Algebra: An Introduction

Published $1978$.

### 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