Book:A.O. Morris/Linear Algebra: An Introduction/Second Edition
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A.O. Morris: Linear Algebra: An Introduction (2nd Edition)
Published $\text {1982}$, Van Nostrand Reinhold
- ISBN 0 442 30541 9
Subject Matter
Contents
- PREFACE
- PREFACE TO THE SECOND EDITION
- 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
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Source work progress
- 1982: A.O. Morris: Linear Algebra: An Introduction (2nd ed.) ... (previous) ... (next): Chapter $1$: Linear Equations and Matrices: $1.3$ Applications to Linear Equations: Corollary $4$