Linear Algebra Student Solutions Manual / Edition 1

Linear Algebra Student Solutions Manual / Edition 1

by Fred Szabo
     
 

ISBN-10: 0126801371

ISBN-13: 9780126801378

Pub. Date: 09/01/2000

Publisher: Elsevier Science

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

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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:
09/01/2000
Edition description:
SOLUTN MN
Pages:
278
Product dimensions:
0.58(w) x 7.50(h) x 9.25(d)

Table of Contents

Preface
1Linear Systems1
Linear Equations1
Linear Systems8
Mathematica and Linear System12
Matrices and Linear Systems14
Augmented Matrices19
Row Echelon Matrices21
Reduced Row Echelon Matrices27
Matrix Equations29
2Matrix Algebra37
Basic Matrix Operations39
A Lexicon of Matrices46
Invertible Matrices52
Orthogonal Matrices57
Lu Decomposition59
Applications70
3Determinants75
The Laplace Expansion75
Applications81
4Vector Spaces89
Real Vector Spaces89
Subspaces110
Complex Vector Spaces117
5Linear Transformations121
Matrices and Linear Transformations131
Images and Kernels139
Similarity151
6Eigenvalues and Eigenvectors153
Characteristic Polynomials159
Eigenspaces165
Diagonalizing Square Matrices169
Applications172
7Norms and Inner Products177
Norms177
Real Inner Products181
Angles191
Quadratic Forms197
Complex Inner Products202
8Orthogonality205
Orthogonal Vectors205
Orthogonal Bases210
Orthonormal Bases212
QR Decomposition218
Orthogonal Matrices224
Orthogonal Subspaces227
Orthogonal Transformations231
The Method of Least Squares236
9Singular Values and Singular Vectors241
Singular Values241
Singular Value Decomposition245
Applications249

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