Linear Algebra With Applications

by Leon, Steven J.

• ISBN13: 9780130337818
• ISBN10: 0130337811
• Edition: 6th
• Format: Paperback
• Copyright: 2002-01-01
• Publisher: PRENTICE HALL

Summary

Written for undergraduate first courses in Linear Algebra. Assumes the user has had calculus. Renowned for thoroughness and accessibility, this top-selling text by one of the leading figures in linear algebra education offers students a challenging and enjoyable study of linear algebra that is infused with an abundance of applications. Balancing coverage of mathematical theory and applied topics, Professor Leon explains concepts with precision so that students at any level can understand the material. Worked examples are heavily integrated into each chapter. The book stresses the important role geometry and visualization play in understanding the subject. This edition will continue to be packaged with the ancillary ATLAST computer exercise guide, as well as new MATLAB and Maple guides.

Table of Contents

Preface	ix
Matrices and Systems of Equations	1	(98)
Systems of Linear Equations	1	(12)
Row Echelon Form	13	(20)
Matrix Algebra	33	(34)
Elementary Matrices	67	(12)
Partitioned Matrices	79	(20)
MATLAB Exercises	91	(6)
Chapter Test	97	(2)
Determinants	99	(26)
The Determinant of a Matrix	99	(8)
Properties of Determinants	107	(8)
Cramer's Rule*	115	(10)
MATLAB Exercises	121	(2)
Chapter Test	123	(2)
Vector Spaces	125	(63)
Definition and Examples	125	(9)
Subspaces	134	(10)
Linear Independence	144	(12)
Basis and Dimension	156	(7)
Change of Basis	163	(11)
Row Space and Column Space	174	(14)
MATLAB Exercises	184	(2)
Chapter Test	186	(2)
Linear Transformations	188	(35)
Definition and Examples	188	(10)
Matrix Representations of Linear Transformations	198	(14)
Similarity	212	(11)
MATLAB Exercises	220	(1)
Chapter Test	221	(2)
Orthogonality	223	(89)
The Scalar Product in Rn	224	(15)
Orthogonal Subspaces	239	(10)
Least Squares Problems	249	(11)
Inner Product Spaces	260	(10)
Orthonormal Sets	270	(20)
The Gram--Schmidt Orthogonalization Process	290	(9)
Orthogonal Polynomials*	299	(13)
MATLAB Exercises	307	(3)
Chapter Test	310	(2)
Eigenvalues	312	(110)
Eigenvalues and Eigenvectors	313	(13)
Systems of Linear Differential Equations	326	(13)
Diagonalization	339	(16)
Hermitian Matrices	355	(12)
The Singular Value Decomposition	367	(15)
Quadratic Forms	382	(15)
Positive Definite Matrices	397	(8)
Nonnegative Matrices*	405	(17)
MATLAB Exercises	412	(9)
Chapter Test	421	(1)
Numerical Linear Algebra	422	(83)
Floating-Point Numbers	423	(4)
Gaussian Elimination	427	(9)
Pivoting Strategies	436	(6)
Matrix Norms and Condition Numbers	442	(16)
Orthogonal Transformations	458	(12)
The Eigenvalue Problem	470	(12)
Least Squares Problems	482	(23)
MATLAB Exercises	494	(9)
Chapter Test	503	(2)
Iterative Methods *Web
Jordan Canonical Form *Web
Appendix: Matlab	505	(12)
Bibliography	517	(3)
Answers To Selected Exercises	520	(20)
Index	540