Cover type: Hardback

Edition: 00

Copyright: 2000

Publisher: Society for Industrial and Applied Mathematics

Published: 2000

International: No

Edition: 00

Copyright: 2000

Publisher: Society for Industrial and Applied Mathematics

Published: 2000

International: No

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Matrix Analysis and Applied Linear Algebra is an honest math text that circumvents the traditional definition-theorem-proof format that has bored students in the past. Meyer uses a fresh approach to introduce a variety of problems and examples ranging from the elementary to the challenging and from simple applications to discovery problems. The focus on applications is a big difference between this book and others. Meyer's book is more rigorous and goes into more depth than some. He includes some of the more contemporary topics of applied linear algebra which are not normally found in undergraduate textbooks. Modern concepts and notation are used to introduce the various aspects of linear equations, leading readers easily to numerical computations and applications. The theoretical developments are always accompanied with examples, which are worked out in detail. Each section ends with a large number of carefully chosen exercises from which the students can gain further insight.

The textbook contains more than 240 examples, 650 exercises, historical notes, and comments on numerical performance and some of the possible pitfalls of algorithms. It comes with a solutions manual that includes complete solutions to all of the exercises. As an added bonus, a CD-ROM is included that contains a searchable copy of the entire textbook and all solutions. Detailed information on topics mentioned in examples, references for additional study, thumbnail sketches and photographs of mathematicians, and a history of linear algebra and computing are also on the CD-ROM, which can be used on all platforms.

Students will love the book's clear presentation and informal writing style. The detailed applications are valuable to them in seeing how linear algebra is applied to real-life situations. One of the most interesting aspects of this book, however, is the inclusion of historical information. These personal insights into some of the greatest mathematicians who developed this subject provide a spark for students and make the teaching of this topic more fun.

Chapter 1: Linear Equations.

Introduction

Gaussian Elimination and Matrices

Gauss-Jordan Method

Two-Point Boundary-Value Problems

Making Gaussian Elimination Work

Ill-Conditioned Systems

Chapter 2: Rectangular Systems and Echelon Forms.

Row Echelon Form and Rank

The Reduced Row Echelon Form

Consistency of Linear Systems

Homogeneous Systems

Nonhomogeneous Systems

Electrical Circuits

Chapter 3: Matrix Algebra.

From Ancient China to Arthur Cayley

Addition, Scalar Multiplication, and Transposition

Linearity

Why Do It This Way?

Matrix Multiplication

Properties of Matrix Multiplication

Matrix Inversion

Inverses of Sums and Sensitivity

Elementary Matrices and Equivalence

The LU Factorization

Chapter 4: Vector Spaces.

Spaces and Subspaces

Four Fundamental Subspaces

Linear Independence

Basis and Dimension

More About Rank

Classical Least Squares

Linear Transformations

Change of Basis and Similarity

Invariant Subspaces

Chapter 5: Norms, Inner Products, and Orthogonality.

Vector Norms

Matrix Norms

Inner Product Spaces

Orthogonal Vectors

Gram-Schmidt Procedure

Unitary and Orthogonal Matrices

Orthogonal Reduction

The Discrete Fourier Transform

Complementary Subspaces

Range-Nullspace Decomposition

Orthogonal Decomposition

Singular Value Decomposition

Orthogonal Projection

Why Least Squares?

Angles Between Subspaces

Chapter 6: Determinants.

Determinants

Additional Properties of Determinants

Chapter 7: Eigenvalues and Eigenvectors.

Elementary Properties of Eigensystems

Diagonalization by Similarity Transformations

Functions of Diagonalizable Matrices

Systems of Differential Equations

Normal Matrices

Positive Definite Matrices

Nilpotent Matrices and Jordan Structure

The Jordan Form

Functions of Non-diagonalizable Matrices

Difference Equations, Limits, and Summability

Minimum Polynomials and Krylov Methods;

Chapter 8: Perron-Frobenius Theory of Nonnegative Matrices.

Introduction

Positive Matrices

Nonnegative Matrices

Stochastic Matrices and Markov Chains.

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Summary

Matrix Analysis and Applied Linear Algebra is an honest math text that circumvents the traditional definition-theorem-proof format that has bored students in the past. Meyer uses a fresh approach to introduce a variety of problems and examples ranging from the elementary to the challenging and from simple applications to discovery problems. The focus on applications is a big difference between this book and others. Meyer's book is more rigorous and goes into more depth than some. He includes some of the more contemporary topics of applied linear algebra which are not normally found in undergraduate textbooks. Modern concepts and notation are used to introduce the various aspects of linear equations, leading readers easily to numerical computations and applications. The theoretical developments are always accompanied with examples, which are worked out in detail. Each section ends with a large number of carefully chosen exercises from which the students can gain further insight.

The textbook contains more than 240 examples, 650 exercises, historical notes, and comments on numerical performance and some of the possible pitfalls of algorithms. It comes with a solutions manual that includes complete solutions to all of the exercises. As an added bonus, a CD-ROM is included that contains a searchable copy of the entire textbook and all solutions. Detailed information on topics mentioned in examples, references for additional study, thumbnail sketches and photographs of mathematicians, and a history of linear algebra and computing are also on the CD-ROM, which can be used on all platforms.

Students will love the book's clear presentation and informal writing style. The detailed applications are valuable to them in seeing how linear algebra is applied to real-life situations. One of the most interesting aspects of this book, however, is the inclusion of historical information. These personal insights into some of the greatest mathematicians who developed this subject provide a spark for students and make the teaching of this topic more fun.

Table of Contents

Chapter 1: Linear Equations.

Introduction

Gaussian Elimination and Matrices

Gauss-Jordan Method

Two-Point Boundary-Value Problems

Making Gaussian Elimination Work

Ill-Conditioned Systems

Chapter 2: Rectangular Systems and Echelon Forms.

Row Echelon Form and Rank

The Reduced Row Echelon Form

Consistency of Linear Systems

Homogeneous Systems

Nonhomogeneous Systems

Electrical Circuits

Chapter 3: Matrix Algebra.

From Ancient China to Arthur Cayley

Addition, Scalar Multiplication, and Transposition

Linearity

Why Do It This Way?

Matrix Multiplication

Properties of Matrix Multiplication

Matrix Inversion

Inverses of Sums and Sensitivity

Elementary Matrices and Equivalence

The LU Factorization

Chapter 4: Vector Spaces.

Spaces and Subspaces

Four Fundamental Subspaces

Linear Independence

Basis and Dimension

More About Rank

Classical Least Squares

Linear Transformations

Change of Basis and Similarity

Invariant Subspaces

Chapter 5: Norms, Inner Products, and Orthogonality.

Vector Norms

Matrix Norms

Inner Product Spaces

Orthogonal Vectors

Gram-Schmidt Procedure

Unitary and Orthogonal Matrices

Orthogonal Reduction

The Discrete Fourier Transform

Complementary Subspaces

Range-Nullspace Decomposition

Orthogonal Decomposition

Singular Value Decomposition

Orthogonal Projection

Why Least Squares?

Angles Between Subspaces

Chapter 6: Determinants.

Determinants

Additional Properties of Determinants

Chapter 7: Eigenvalues and Eigenvectors.

Elementary Properties of Eigensystems

Diagonalization by Similarity Transformations

Functions of Diagonalizable Matrices

Systems of Differential Equations

Normal Matrices

Positive Definite Matrices

Nilpotent Matrices and Jordan Structure

The Jordan Form

Functions of Non-diagonalizable Matrices

Difference Equations, Limits, and Summability

Minimum Polynomials and Krylov Methods;

Chapter 8: Perron-Frobenius Theory of Nonnegative Matrices.

Introduction

Positive Matrices

Nonnegative Matrices

Stochastic Matrices and Markov Chains.

Publisher Info

Publisher: Society for Industrial and Applied Mathematics

Published: 2000

International: No

Published: 2000

International: No

The textbook contains more than 240 examples, 650 exercises, historical notes, and comments on numerical performance and some of the possible pitfalls of algorithms. It comes with a solutions manual that includes complete solutions to all of the exercises. As an added bonus, a CD-ROM is included that contains a searchable copy of the entire textbook and all solutions. Detailed information on topics mentioned in examples, references for additional study, thumbnail sketches and photographs of mathematicians, and a history of linear algebra and computing are also on the CD-ROM, which can be used on all platforms.

Students will love the book's clear presentation and informal writing style. The detailed applications are valuable to them in seeing how linear algebra is applied to real-life situations. One of the most interesting aspects of this book, however, is the inclusion of historical information. These personal insights into some of the greatest mathematicians who developed this subject provide a spark for students and make the teaching of this topic more fun.

Chapter 1: Linear Equations.

Introduction

Gaussian Elimination and Matrices

Gauss-Jordan Method

Two-Point Boundary-Value Problems

Making Gaussian Elimination Work

Ill-Conditioned Systems

Chapter 2: Rectangular Systems and Echelon Forms.

Row Echelon Form and Rank

The Reduced Row Echelon Form

Consistency of Linear Systems

Homogeneous Systems

Nonhomogeneous Systems

Electrical Circuits

Chapter 3: Matrix Algebra.

From Ancient China to Arthur Cayley

Addition, Scalar Multiplication, and Transposition

Linearity

Why Do It This Way?

Matrix Multiplication

Properties of Matrix Multiplication

Matrix Inversion

Inverses of Sums and Sensitivity

Elementary Matrices and Equivalence

The LU Factorization

Chapter 4: Vector Spaces.

Spaces and Subspaces

Four Fundamental Subspaces

Linear Independence

Basis and Dimension

More About Rank

Classical Least Squares

Linear Transformations

Change of Basis and Similarity

Invariant Subspaces

Chapter 5: Norms, Inner Products, and Orthogonality.

Vector Norms

Matrix Norms

Inner Product Spaces

Orthogonal Vectors

Gram-Schmidt Procedure

Unitary and Orthogonal Matrices

Orthogonal Reduction

The Discrete Fourier Transform

Complementary Subspaces

Range-Nullspace Decomposition

Orthogonal Decomposition

Singular Value Decomposition

Orthogonal Projection

Why Least Squares?

Angles Between Subspaces

Chapter 6: Determinants.

Determinants

Additional Properties of Determinants

Chapter 7: Eigenvalues and Eigenvectors.

Elementary Properties of Eigensystems

Diagonalization by Similarity Transformations

Functions of Diagonalizable Matrices

Systems of Differential Equations

Normal Matrices

Positive Definite Matrices

Nilpotent Matrices and Jordan Structure

The Jordan Form

Functions of Non-diagonalizable Matrices

Difference Equations, Limits, and Summability

Minimum Polynomials and Krylov Methods;

Chapter 8: Perron-Frobenius Theory of Nonnegative Matrices.

Introduction

Positive Matrices

Nonnegative Matrices

Stochastic Matrices and Markov Chains.