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# Linear Algebra With Applications

**by**Leon, Steven J.

6th

### 9780130337832

0130337838

Paperback

1/1/2002

Prentice Hall

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## Summary

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

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 |

Table of Contents provided by Syndetics. All Rights Reserved. |