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Linear Algebra With Applications

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  • Edition: 6th
  • Format: Paperback
  • Copyright: 2002-01-01
  • Publisher: Pearson College Div
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Renowned for its thoroughness, clarity, and accessibility, this best-selling book by one of today's leading figures in linear algebra reform offers users a challenging yet enjoyable treatment of linear algebra that is infused with an abundance of applications and worked examples. Balancing coverage of mathematical theory and applied topics, the book stresses the important role geometry and visualization play in understanding the subject, and now comes with the new ancillary ATLAS computer exercise guide.Provides modern and comprehensive coverage of the subject, spanning all topics in the core syllabus recommended by the NSF sponsored Linear Algebra Curriculum Study Group. Offers new applications in astronomy and statistics, emphasizes the use of geometry to visualize linear algebra and aid in understanding all of the major topics, and previews some of the more difficult vector space concepts early on. MATLAB computing exercises provide users with experience performing matrix computations.For mathematicians.

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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