Carl Meyer: Matrix Analysis - Download Chapters

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TABLE OF CONTENTS (pdf format 92K)

Preface (pdf format 100K)

INDEX (pdf format 132K)

Chapter 1, LINEAR EQUATIONS (pdf format 356K)

1.1 Introduction

1.2 Gaussian Elimination And Matrices

1.3 Gauss-Jordan Method

1.4 Two-Point Boundary-Value Problems

1.5 Making Gaussian Elimination Work

1.6 Ill-Conditioned Systems

Chapter 2, RECTANGULAR SYSTEMS AND ECHELON FORMS (pdf format 348K)

2.1 Row Echelon Form And Rank

2.2 The Reduced Row Echelon Form

2.3 Consistency Of Linear Systems

2.4 Homogeneous Systems

2.5 Nonhomogeneous Systems

2.6 Electrical Circuits

Chapter 3, MATRIX ALGEBRA (pdf format 616K)

3.1 From Ancient China To Arthur Cayley

3.2 Addition, Scalar Multiplication, And Transposition

3.3 Linearity

3.4 Why Do It This Way

3.5 Matrix Multiplication

3.6 Properties Of Matrix Multiplication

3.7 Matrix Inversion

3.8 Inverses Of Sums and Sensitivity

3.9 Elementary Matrices And Equivalence

3.10 The LU Factorization

Chapter 4, VECTOR SPACES (pdf format 724K)

4.1 Spaces And Subspaces

4.2 Four Fundamental Subspaces

4.3 Linear Independence

4.4 Basis And Dimension

4.5 More About Rank

4.6 Classical Least Squares

4.7 Linear Transformations

4.8 Change Of Basis And Similarity

4.9 Invariant Subspaces

Chapter 5, NORMS, INNER PRODUCTS, AND ORTHOGONALITY (pdf format 1.2M)

5.1 Vector Norms

5.2 Matrix Norms

5.3 Inner Product Spaces

5.4 Orthogonal Vectors

5.5 Gram ĐSchmidt Procedure

5.6 Unitary and Orthogonal Matrices

5.7 Orthogonal Reduction

5.8 The Discrete Fourier Transform

5.9 Complementary Subspaces

5.10 Range-Nullspace Decomposition

5.11 Orthogonal Decomposition

5.12 Singular Value Decomposition

5.13 Orthogonal Projection

5.14 Why Least Squares?

5.15 Angles Between Subspaces

Chapter 6, DETERMINANTS (pdf format 352K)

6.1 Determinants

6.2 Additional Properties Of Determinants

Chapter 7, EIGENVALUES AND EIGENVECTORS (pdf format 1.1M)

7.1 Elementary Properties Of Eigensystems

7.2 Diagonalization by Similarity Transformations

7.3 Functions Of Diagonalizable Matrices

7.4 Systems Of Differential Equations

7.5 Normal Matrices

7.6 Positive Definite Matrices

7.7 Nilpotent Matrices and Jordan Structure

7.8 The Jordan Form

7.9 Functions Of Non-diagonalizable Matrices

7.10 Difference Equations, Limits, And Summability

7.11 Minimum Polynomials and Krylov Methods

Chapter 8, Perron-Frobenius Theory Of Nonnegative Matrices (pdf format 440K)

8.1 Introduction

8.2 Positive Matrices

8.3 Nonnegative Matrices

8.4 Stochastic Matrices and Markov Chains

Solutions Manual (pdf format 952K)