Linear Algebra With Applications

by Cullen, Charles G.

• ISBN13: 9780673993861
• ISBN10: 0673993868
• Edition: 2nd
• Format: Paperback
• Copyright: 1997-01-08
• Publisher: Pearson

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