Linear Algebra with Mathematica

by Szabo

• ISBN13: 9780126801354
• ISBN10: 0126801355
• Format: Hardcover
• Copyright: 2000-01-31
• Publisher: Elsevier Science

Summary

Linear Algebra: An Introduction with Mathematica uses a matrix-based presentation and covers the standard topics any mathematician will need to understand linear algebra while using Mathematica. Development of analytical and computational skills is emphasized, and worked examples provide step-by-step methods for solving basic problems using Mathematica. The subject's rich pertinence to problem solving across disciplines is illustrated with applications in engineering, the natural sciences, computer animation, and statistics. * Includes a thematic presentation of linear algebra * Provides a systematic integration of Mathematica * Encourages students to appreciate the benefits of mathematical rigor * All exercises can be solved with Mathematica

Table of Contents

Using Mathematica	1	(14)
Linear Systems	15	(88)
Linear Equations	15	(13)
Linear Systems	28	(9)
Mathematica and Linear Systems	37	(6)
Matrices and Linear Systems	43	(11)
Augmented Matrices	54	(8)
Row Echelon Matrices	62	(7)
Reduced Row Echelon Matrices	69	(5)
Matrix Equations	74	(16)
Applications	90	(11)
Review	101	(2)
Matrix Algebra	103	(104)
Introduction	103	(5)
Basic Matrix Operations	108	(17)
A Lexicon of Matrices	125	(13)
Invertible Matrices	138	(11)
Orthogonal Matrices	149	(3)
Lu Decomposition	152	(21)
Applications	173	(30)
Review	203	(4)
Determinants	207	(40)
The Laplace Expansion	207	(17)
Applications	224	(20)
Review	244	(3)
Vector Spaces	247	(74)
Real Vector Spaces	247	(8)
Bases And Dimension	255	(36)
Subspaces	291	(24)
Complex Vector Spaces	315	(3)
Review	318	(3)
Linear Transformations	321	(54)
Linear Transformations	321	(21)
Matrices of Linear Transformations	342	(11)
Images and Kernels	353	(14)
Similarity	367	(4)
Review	371	(4)
Eigenvalues and Eigenvectors	375	(62)
Introduction	375	(8)
Characteristic Polynomials	383	(15)
Eigenspaces	398	(14)
Diagonalizing Square Matrices	412	(7)
Applications	419	(15)
Review	434	(3)
Norms and Inner Products	437	(54)
Norms	438	(12)
Real Inner Products	450	(11)
Angles	461	(9)
Quadratic Forms	470	(15)
Complex Inner Products	485	(3)
Review	488	(3)
Orthogonality	491	(68)
Orthogonal Vectors	491	(9)
Orthogonal Bases	500	(5)
Orthonormal Bases	505	(5)
Or Decomposition	510	(12)
Orthogonal Matrices	522	(6)
Orthogonal Subspaces	528	(6)
Orthogonal Transformations	534	(13)
The Method of Least Squares	547	(7)
Review	554	(5)
Singular Values and Singular Vectors	559	(1)
Singular Values	559	(4)
Singular Value Decomposition	563	(7)
Applications	570	(20)
Review	590	(1)
APPENDICES
A The Fundamental Theorem of Algebra	A-1	(1)
B Numerical Calculations	B-1	(1)
C Mathematical Induction	C-1	(1)
D Sigma Notation	D-1	(1)
E Mathematica Packages and Defined Functions	E-1	(1)
F Answers To Selected Exercises	F-1	(1)
Index	I-1