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9780673993861

Linear Algebra With Applications

by
  • ISBN13:

    9780673993861

  • ISBN10:

    0673993868

  • Edition: 2nd
  • Format: Paperback
  • Copyright: 1997-01-08
  • Publisher: Pearson
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List Price: $119.99

Summary

This clear, unintimidating introductory text is distinguished by its strong computational and applied approach. Suitable for a sophomore-level course in linear, matrix, or computational algebra, it prepares students for further study in mathematics, computer science, chemistry, or economics. An outstanding interactive software package, specifically developed to accompany this text, offers ease of use, power, and flexibility, focusing attention on the interpretation of calculations rather than on the calculations themselves. The Second Edition has been improved by including more applications, more motivation to discussions, more graphics, and discussions of various relevant software packages, and the TI-85 graphics calculator.

Table of Contents

Preface ix
1 Linear Systems and Matrices
1(97)
1.1 Geometric View of Linear Systems
1(12)
1.2 Gaussian and Gauss-Jordan Elimination
13(11)
1.3 Row Equivalence and Echelon Matrices
24(13)
1.4 Homogeneous Systems
37(8)
1.5 Matrix Algebra
45(13)
1.6 Properties of Matrix Operations
58(8)
1.7 Row Equivalence and Matrix Multiplication
66(11)
1.8 The LU Factorization (Optional)
77(10)
1.9 Partial Pivoting (Optional)
87(11)
2 Determinants
98(38)
2.1 Definitions and Examples
98(9)
2.2 Evaluation of det (A): A Better Way
107(9)
2.3 Additional Properties of Determinants
116(9)
2.4 Eigenvalues and Eigenvectors
125(11)
3 Vector Spaces
136(95)
3.1 XXX(2) and XXX(3): Old Friends
136(15)
3.2 Euclidean n-space and its Subspaces
151(9)
3.3 Subspaces of XXX(n)--Continued
160(8)
3.4 Linear Independence and Dependence in XXX(n)
168(6)
3.5 Basis and Dimension
174(9)
3.6 Orthogonality in XXX(n)
183(14)
3.7 Vector Spaces--The General Concept
197(7)
3.8 Subspaces
204(10)
3.9 Linear Independence, Basis, and Dimension
214(17)
4 Linear Transformations
231(70)
4.1 Definitions and Examples
231(11)
4.2 The Range and Null Space of a Linear Transformation
242(10)
4.3 The Algebra of Linear Transformations
252(6)
4.4 Geometric Interpretation
258(14)
4.5 Matrices and Linear Transformations
272(9)
4.6 Change of Basis (Optional)
281(7)
4.7 The Change-of-Basis Problem (Optional)
288(13)
5 Similar Matrices and the Eigenvalue Problem
301(40)
5.1 Diagonalization--Eigenvalues and Eigenvectors
301(12)
5.2 Orthogonal Similarity and Symmetric Matrices
313(9)
5.3 Schur's Theorem (Optional)
322(7)
5.4 The Power Method (Optional)
329(12)
6 Linear Programming
341(40)
6.1 The Geometric Point of View
341(12)
6.2 Different Types of Linear Programming Problems
353(8)
6.3 The Simplex Method
361(12)
6.4 Refinements of the Simplex Method
373(8)
7 Selected Applications
381(37)
7.1 Graph Theory
381(9)
7.2 Least Squares Approximations
390(11)
7.3 Quadratic Forms
401(9)
7.4 Linear Economic Models
410(8)
Appendix A Linear Algebra Software 418(3)
Appendix B The MATMAN Program 421(22)
Appendix C The MATALG Program 443(14)
Appendix D The MATLAB Program 457(11)
Answers to Odd-numbered Exercises 468(25)
Index 493

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