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

A.O. Morris: Linear Algebra: An Introduction

Published $\text {1978}$

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

Further Editions

• 1982: A.O. Morris: Linear Algebra: An Introduction (2nd ed.)