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Matrix Analysis and Applied Linear Algebra - With Solutions Manual and CD

Matrix Analysis and Applied Linear Algebra - With Solutions Manual and CD - 00 edition

Matrix Analysis and Applied Linear Algebra - With Solutions Manual and CD - 00 edition

ISBN13: 9780898714548

ISBN10: 0898714540

Matrix Analysis and Applied Linear Algebra - With Solutions Manual and CD by Carl D. Meyer - ISBN 9780898714548
Cover type: Hardback
Edition: 00
Copyright: 2000
Publisher: Society for Industrial and Applied Mathematics
Published:
International: No
Matrix Analysis and Applied Linear Algebra - With Solutions Manual and CD by Carl D. Meyer - ISBN 9780898714548

ISBN13: 9780898714548

ISBN10: 0898714540

Cover type: Hardback
Edition: 00
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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

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.