9780130337818

Linear Algebra With Applications

by
  • ISBN13:

    9780130337818

  • ISBN10:

    0130337811

  • Edition: 6th
  • Format: Paperback
  • Copyright: 1/1/2002
  • Publisher: PRENTICE HALL
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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

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