Matrix Analysis and Applied Linear Algebra

ISBN-10: 0898714540
ISBN-13: 9780898714548
Edition: 2000
Authors: Carl Meyer
List price: $80.50
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Description: This book avoids the traditional definition-theorem-proof format; instead a fresh approach introduces a variety of problems and examples all in a clear and informal style. The in-depth focus on applications separates this book from others, and helps  More...

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Book details

List price: $80.50
Copyright year: 2000
Publisher: Society for Industrial and Applied Mathematics
Binding: Hardcover
Pages: 730
Size: 9.25" wide x 9.75" long x 0.50" tall
Weight: 4.840
Language: English

This book avoids the traditional definition-theorem-proof format; instead a fresh approach introduces a variety of problems and examples all in a clear and informal style. The in-depth focus on applications separates this book from others, and helps students to see how linear algebra can be applied to real-life situations. Some of the more contemporary topics of applied linear algebra are included here which are not normally found in undergraduate textbooks. Theoretical developments are always accompanied with detailed examples, and each section ends with a number of exercises from which students can gain further insight. Moreover, the inclusion of historical information provides personal insights into the mathematicians who developed this subject. The textbook contains numerous examples and exercises, historical notes, and comments on numerical performance and the possible pitfalls of algorithms. Solutions to all of the exercises are provided, as well as a CD-ROM containing a searchable copy of the textbook.

Preface
Linear Equations
Introduction
Gaussian Elimination and Matrices
Gauss-Jordan Method
Two-Point Boundary Value Problems
Making Gaussian Elimination Work
Ill-Conditioned Systems
Rectangular Systems and Echelon Forms
Row Echelon Form and Rank
Reduced Row Echelon Form
Consistency of Linear Systems
Homogeneous Systems
Nonhomogeneous Systems
Electrical Circuits
Matrix Algebra
From Ancient China to Arthur Cayley
Addition 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
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
Norms, Inner Products, and Orthogonality
Vector Norms
Matrix Norms
Inner-Product Spaces
Orthogonal Vectors
Gram-Schmidt Procedure
Unitary and Orthogonal Matrices
Orthogonal Reduction
Discrete Fourier Transform
Complementary Subspaces
Range-Nullspace Decomposition
Orthogonal Decomposition
Singular Value Decomposition
Orthogonal Projection
Why Least Squares?
Angles between Subspaces
Determinants
Determinants
Additional Properties of Determinants
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
Jordan Form
Functions of Nondiagonalizable Matrices
Difference Equations, Limits, and Summability
Minimum Polynomials and Krylov Methods
Perron-Frobenius Theory
Introduction
Positive Matrices
Nonnegative Matrices
Stochastic Matrices and Markov Chains
Index

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