9780131857858

Linear Algebra with Applications

by
  • ISBN13:

    9780131857858

  • ISBN10:

    0131857851

  • Edition: 7th
  • Format: Hardcover
  • Copyright: 1/1/2010
  • Publisher: Prentice Hall
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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

Prefacep. ix
Matrices and Systems of Equationsp. 1
Systems of Linear Equationsp. 1
Row Echelon Formp. 13
Matrix Algebrap. 33
Elementary Matricesp. 67
Partitioned Matricesp. 79
Matlab Exercisesp. 91
Chapter Testp. 97
Determinantsp. 99
The Determinant of a Matrixp. 99
Properties of Determinantsp. 107
Cramer's Rulep. 115
Matlab Exercisesp. 121
Chapter Testp. 123
Vector Spacesp. 125
Definition and Examplesp. 125
Subspacesp. 134
Linear Independencep. 144
Basis and Dimensionp. 156
Change of Basisp. 163
Row Space and Column Spacep. 174
Matlab Exercisesp. 184
Chapter Testp. 186
Linear Transformationsp. 188
Definition and Examplesp. 188
Matrix Representations of Linear Transformationsp. 198
Similarityp. 212
Matlab Exercisesp. 220
Chapter Testp. 221
Orthogonalityp. 223
The Scalar Product in R[superscript n]p. 224
Orthogonal Subspacesp. 239
Least Squares Problemsp. 249
Inner Product Spacesp. 260
Orthonormal Setsp. 270
The Gram--Schmidt Orthogonalization Processp. 290
Orthogonal Polynomialsp. 299
Matlab Exercisesp. 307
Chapter Testp. 310
Eigenvaluesp. 312
Eigenvalues and Eigenvectorsp. 313
Systems of Linear Differential Equationsp. 326
Diagonalizationp. 339
Hermitian Matricesp. 355
The Singular Value Decompositionp. 367
Quadratic Formsp. 382
Positive Definite Matricesp. 397
Nonnegative Matricesp. 405
Matlab Exercisesp. 412
Chapter Testp. 421
Numerical Linear Algebrap. 422
Floating-Point Numbersp. 423
Gaussian Eliminationp. 427
Pivoting Strategiesp. 436
Matrix Norms and Condition Numbersp. 442
Orthogonal Transformationsp. 458
The Eigenvalue Problemp. 470
Least Squares Problemsp. 482
Matlab Exercisesp. 494
Chapter Testp. 503
Iterative Methods *Web
Jordan Canonical Form *Web
Matlabp. 505
Bibliographyp. 517
Answers to Selected Exercisesp. 520
Indexp. 540
Table of Contents provided by Syndetics. All Rights Reserved.

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