9780898714548

Matrix Analysis and Applied Linear Algebra

by
  • ISBN13:

    9780898714548

  • ISBN10:

    0898714540

  • Edition: CD
  • Format: Hardcover
  • Copyright: 6/1/2000
  • Publisher: Society for Industrial & Applied
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Summary

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.

Author Biography

Carl Meyer is a Professor in the Department of Mathematics at North Carolina State University

Table of Contents

Preface ix
Linear Equations
1(40)
Introduction
1(2)
Gaussian Elimination and Matrices
3(12)
Gauss--Jordan Method
15(3)
Two-Point Boundary Value Problems
18(3)
Making Gaussian Elimination Work
21(12)
III-Conditioned Systems
33(8)
Rectangular Systems and Echelon Forms
41(38)
Row Echelon Form and Rank
41(6)
Reduced Row Echelon Form
47(6)
Consistency of Linear Systems
53(4)
Homogeneous Systems
57(7)
Nonhomogeneous Systems
64(9)
Electrical Circuits
73(6)
Matrix Algebra
79(80)
From Ancient China to Arthur Cayley
79(2)
Addition and Transposition
81(8)
Linearity
89(4)
Why Do it this Way
93(2)
Matrix Multiplication
95(10)
Properties of Matrix Multiplication
105(10)
Matrix Inversion
115(9)
Inverses of Sums and Sensitivity
124(7)
Elementary Matrices and Equivalence
131(10)
The LU Factorization
141(18)
Vector Spaces
159(110)
Spaces and Subspaces
159(10)
Four Fundamental Subspaces
169(12)
Linear Independence
181(13)
Basis and Dimension
194(16)
More about Rank
210(13)
Classical Least Squares
223(15)
Linear Transformations
238(13)
Change of Basis and Similarity
251(8)
Invariant Subspaces
259(10)
Norms, Inner Products, and Orthogonality
269(190)
Vector Norms
269(10)
Matrix Norms
279(7)
Inner-Product Spaces
286(8)
Orthogonal Vectors
294(13)
Gram--Schmidt Procedure
307(13)
Unitary and Orthogonal Matrices
320(21)
Orthogonal Reduction
341(15)
Discrete Fourier Transform
356(27)
Complementary Subspaces
383(11)
Range-Nullspace Decomposition
394(9)
Orthogonal Decomposition
403(8)
Singular Value Decomposition
411(18)
Orthogonal Projection
429(17)
Why Least Squares?
446(4)
Angles between Subspaces
450(9)
Determinants
459(30)
Determinants
459(16)
Additional Properties of Determinants
475(14)
Eigenvalues and Eigenvectors
489(172)
Elementary Properties of Eigensystems
489(16)
Diagonalization by Similarity Transformations
505(20)
Functions of Diagonalizable Matrices
525(16)
Systems of Differential Equations
541(6)
Normal Matrices
547(11)
Positive Definite Matrices
558(16)
Nilpotent Matrices and Jordan Structure
574(13)
Jordan Form
587(12)
Functions of Nondiagonalizable Matrices
599(17)
Difference Equations, Limits, and Summability
616(26)
Minimum Polynomials and Krylov Methods
642(19)
Perron--Frobenius Theory
661(44)
Introduction
661(2)
Positive Matrices
663(7)
Nonnegative Matrices
670(17)
Stochastic Matrices and Markov Chains
687(18)
Index 705

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