Linear Algebra with Mathematica, Student Solutions Manual

by Szabo

• ISBN13: 9780126801378
• ISBN10: 0126801371
• Edition: Answer
• Format: Paperback
• Copyright: 2000-09-07
• Publisher: Elsevier Science

Summary

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

Table of Contents

Preface	ix
Linear Systems	1	(36)
Linear Equations	1	(7)
Linear Systems	8	(4)
Mathematica and Linear System	12	(2)
Matrices and Linear Systems	14	(5)
Augmented Matrices	19	(2)
Row Echelon Matrices	21	(6)
Reduced Row Echelon Matrices	27	(2)
Matrix Equations	29	(8)
Matrix Algebra	37	(38)
Basic Matrix Operations	39	(7)
A Lexicon of Matrices	46	(6)
Invertible Matrices	52	(5)
Orthogonal Matrices	57	(2)
Lu Decomposition	59	(11)
Applications	70	(5)
Determinants	75	(14)
The Laplace Expansion	75	(6)
Applications	81	(8)
Vector Spaces	89	(32)
Real Vector Spaces	89	(21)
Subspaces	110	(7)
Complex Vector Spaces	117	(4)
Linear Transformations	121	(32)
Matrices and Linear Transformations	131	(8)
Images and Kernels	139	(12)
Similarity	151	(2)
Eigenvalues and Eigenvectors	153	(24)
Characteristic Polynomials	159	(6)
Eigenspaces	165	(4)
Diagonalizing Square Matrices	169	(3)
Applications	172	(5)
Norms and Inner Products	177	(28)
Norms	177	(4)
Real Inner Products	181	(10)
Angles	191	(6)
Quadratic Forms	197	(5)
Complex Inner Products	202	(3)
Orthogonality	205	(36)
Orthogonal Vectors	205	(5)
Orthogonal Bases	210	(2)
Orthonormal Bases	212	(6)
Qr Decomposition	218	(6)
Orthogonal Matrices	224	(3)
Orthogonal Subspaces	227	(4)
Orthogonal Transformations	231	(5)
The Method of Least Squares	236	(5)
Singular Values and Singular Vectors	241	(8)
Singular Values	241	(4)
Singular Value Decomposition	245	(4)
Applications	249