Linear Algebra with Mathematica, Student Solutions Manual: An Introduction Using Mathematica / Edition 1

by Fred Szabo

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.

Product Details

ISBN-13:	9780126801378
Publisher:	Elsevier Science
Publication date:	09/07/2000
Edition description:	SOLUTN MN
Pages:	267
Product dimensions:	7.38(w) x 9.25(h) x (d)

About the Author

Author of:

The Linear Algebra Survival Guide, 1st Edition

Actuaries' Survival Guide, 2nd Edition

Actuaries' Survival Guide, 1st Edition

Linear Algebra: An Introduction using Maple, 1st Edition

Linear Algebra: An Introduction using Mathematica, 1st Edition

Fred E. Szabo is professor in the Department of Mathematics and Statistics at Concordia University in Canada. He completed his undergraduate studies at Oxford University under the guidance of Sir Michael Dummett and received a Ph.D. in mathematics from McGill University under the supervision of Joachim Lambek. After postdoctoral studies at Oxford University and visiting professorships at several European universities, he returned to Concordia University as a faculty member and dean of graduate studies. For more than twenty years, he developed methods for the teaching of mathematics with technology. In 2012 he was honored at the annual Wolfram Technology Conference for his work on "A New Kind of Learning" with a Wolfram Innovator Award. He is currently professor and Provost Fellow at Concordia University.

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