Linear Algebra with Applications

by Leon, Steve

• ISBN13: 9780131857858
• ISBN10: 0131857851
• Edition: 7th
• Format: Hardcover
• Copyright: 2010-01-01
• Publisher: Prentice Hall

Summary

This thorough and accessible book from one of the leading figures in the field of linear algebra provides readers with both a challenging and broad understanding of linear algebra. The author infuses key concepts with their modern practical applications to offer readers examples of how mathematics is used in the real world. Topics such as linear systems theory, matrix theory, and vector space theory are integrated with real world applications to give a clear understanding of the material and the application of the concepts to solve real world problems. Each chapter contains integrated worked examples and chapter tests. The book stresses the important role geometry and visualization play in understanding linear algebra.For anyone interested in the application of linear algebra theories to solve real world problems.

Table of Contents

Preface	p. ix
Matrices and Systems of Equations	p. 1
Systems of Linear Equations	p. 1
Row Echelon Form	p. 13
Matrix Algebra	p. 33
Elementary Matrices	p. 67
Partitioned Matrices	p. 79
Matlab Exercises	p. 91
Chapter Test	p. 97
Determinants	p. 99
The Determinant of a Matrix	p. 99
Properties of Determinants	p. 107
Cramer's Rule	p. 115
Matlab Exercises	p. 121
Chapter Test	p. 123
Vector Spaces	p. 125
Definition and Examples	p. 125
Subspaces	p. 134
Linear Independence	p. 144
Basis and Dimension	p. 156
Change of Basis	p. 163
Row Space and Column Space	p. 174
Matlab Exercises	p. 184
Chapter Test	p. 186
Linear Transformations	p. 188
Definition and Examples	p. 188
Matrix Representations of Linear Transformations	p. 198
Similarity	p. 212
Matlab Exercises	p. 220
Chapter Test	p. 221
Orthogonality	p. 223
The Scalar Product in R[superscript n]	p. 224
Orthogonal Subspaces	p. 239
Least Squares Problems	p. 249
Inner Product Spaces	p. 260
Orthonormal Sets	p. 270
The Gram--Schmidt Orthogonalization Process	p. 290
Orthogonal Polynomials	p. 299
Matlab Exercises	p. 307
Chapter Test	p. 310
Eigenvalues	p. 312
Eigenvalues and Eigenvectors	p. 313
Systems of Linear Differential Equations	p. 326
Diagonalization	p. 339
Hermitian Matrices	p. 355
The Singular Value Decomposition	p. 367
Quadratic Forms	p. 382
Positive Definite Matrices	p. 397
Nonnegative Matrices	p. 405
Matlab Exercises	p. 412
Chapter Test	p. 421
Numerical Linear Algebra	p. 422
Floating-Point Numbers	p. 423
Gaussian Elimination	p. 427
Pivoting Strategies	p. 436
Matrix Norms and Condition Numbers	p. 442
Orthogonal Transformations	p. 458
The Eigenvalue Problem	p. 470
Least Squares Problems	p. 482
Matlab Exercises	p. 494
Chapter Test	p. 503
Iterative Methods *Web
Jordan Canonical Form *Web
Matlab	p. 505
Bibliography	p. 517
Answers to Selected Exercises	p. 520
Index	p. 540
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