Linear Algebra Student Solutions Manual / Edition 1

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Overview

This book introduces interested readers, practitioners, and researchers to Mathematica methods for solving practical problems in linear algebra. It contains step-by-step solutions of problems in computer science, economics, engineering, mathematics, statistics, and other areas of application. Each chapter contains both elementary and more challenging problems, grouped by fields of application, and ends with a set of exercises. Selected answers are provided in an appendix. The book contains a glossary of definitions and theorem, as well as a summary of relevant Mathematica tools. Applications of Linear Algebra can be used both in laboratory sessions and as a source of take-home problems and projects.


* Concentrates on problem solving and aims to increase the readers' analytical skills
* Provides ample opportunities for applying theoretical results and transferring knowledge between different areas of application; Mathematica plays a key role in this process
* Makes learning fun and builds confidence
* Allows readers to tackle computationally challenging problems by minimizing the frustration caused by the arithmetic intricacies of numerical linear algebra

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Product Details

  • ISBN-13: 9780126801378
  • Publisher: Elsevier Science
  • Publication date: 9/1/2000
  • Edition description: SOLUTN MN
  • Edition number: 1
  • Pages: 278
  • Product dimensions: 0.58 (w) x 7.50 (h) x 9.25 (d)

Table of Contents

Preface
1 Linear Systems 1
Linear Equations 1
Linear Systems 8
Mathematica and Linear System 12
Matrices and Linear Systems 14
Augmented Matrices 19
Row Echelon Matrices 21
Reduced Row Echelon Matrices 27
Matrix Equations 29
2 Matrix Algebra 37
Basic Matrix Operations 39
A Lexicon of Matrices 46
Invertible Matrices 52
Orthogonal Matrices 57
Lu Decomposition 59
Applications 70
3 Determinants 75
The Laplace Expansion 75
Applications 81
4 Vector Spaces 89
Real Vector Spaces 89
Subspaces 110
Complex Vector Spaces 117
5 Linear Transformations 121
Matrices and Linear Transformations 131
Images and Kernels 139
Similarity 151
6 Eigenvalues and Eigenvectors 153
Characteristic Polynomials 159
Eigenspaces 165
Diagonalizing Square Matrices 169
Applications 172
7 Norms and Inner Products 177
Norms 177
Real Inner Products 181
Angles 191
Quadratic Forms 197
Complex Inner Products 202
8 Orthogonality 205
Orthogonal Vectors 205
Orthogonal Bases 210
Orthonormal Bases 212
QR Decomposition 218
Orthogonal Matrices 224
Orthogonal Subspaces 227
Orthogonal Transformations 231
The Method of Least Squares 236
9 Singular Values and Singular Vectors 241
Singular Values 241
Singular Value Decomposition 245
Applications 249
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