Introductory Linear Algebra With Applications

by Kolman, Bernard; Hill, David R.

• ISBN13: 9780132663137
• ISBN10: 0132663139
• Edition: 6th
• Format: Hardcover
• Copyright: 1997-02-01
• Publisher: Prentice Hall Professional Technical Reference

Summary

This is the easier of Kolman's two texts: it has more applications and vector spaces come later in the text. Major revision. New edition is most technology friendly book in this market. Last chapter is on numerical techniques using MATLAB. Also has superb MATLAB manual by Hill/Zitarelli ('96) that should be sampled to anyone interested in technology.

Table of Contents

Preface	xi
Part I INTRODUCTORY LINEAR ALGEBRA	3	(368)
1 Linear Equations and Matrices	3	(88)
1.1 Linear Systems	3	(8)
1.2 Matrices	11	(7)
1.3 Dot Product and Matrix Multiplication	18	(17)
1.4 Properties of Matrix Operations	35	(12)
1.5 Solutions of Linear Systems of Equations	47	(22)
1.6 The Inverse of a Matrix	69	(22)
2 Determinants	91	(32)
2.1 Definition and Properties	91	(12)
2.2 Cofactor Expansion and Applications	103	(15)
2.3 Determinants from a Computational Point of View	118	(5)
3 Vectors in R(2) and R(n)	123	(74)
3.1 Vectors in the Plane	123	(18)
3.2 n-Vectors	141	(17)
3.3 Introduction to Linear Transformations	158	(13)
3.4 Computer Graphics (Optional)	171	(8)
3.5 Cross Product in R(3) (Optional)	179	(7)
3.6 Lines and Planes	186	(11)
4 Real Vector Spaces	197	(94)
4.1 Real Vector Spaces	197	(6)
4.2 Subspaces	203	(10)
4.3 Linear Independence	213	(11)
4.4 Basis and Dimension	224	(13)
4.5 Homogeneous Systems	237	(7)
4.6 The Rank of a Matrix and Applications	244	(11)
4.7 Coordinates and Change of Basis	255	(14)
4.8 Orthonormal Bases in R(n)	269	(8)
4.9 Orthogonal Complements	277	(14)
5 Eigenvalues and Eigenvectors	291	(36)
5.1 Diagonalization	291	(21)
5.2 Diagonalization of Symmetric Matrices	312	(15)
6 Linear Transformations and Matrices	327	(39)
6.1 Definition and Examples	327	(7)
6.2 The Kernel and Range of a Linear Transformation	334	(11)
6.3 The Matrix of a Linear Transformation	345	(21)
Cumulative Review of Part I	366	(5)
Part II APPLICATIONS	371	(164)
7 Linear Programming	371	(46)
7.1 The Linear Programming Problem; Geometric Solution	371	(18)
7.2 The Simplex Method	389	(19)
7.3 Duality	408	(9)
8 Applications	417	(118)
8.1 Graph Theory	417	(17)
8.2 Electrical Circuits	434	(5)
8.3 Markov Chains	439	(11)
8.4 Least Squares	450	(11)
8.5 Linear Economic Models	461	(8)
8.6 Differential Equations (Calculus Required)	469	(11)
8.7 The Fibonacci Sequence	480	(4)
8.8 Quadratic Forms	484	(9)
8.9 Conic Sections	493	(8)
8.10 Quadric Surfaces	501	(10)
8.11 The Theory of Games	511	(24)
Part III NUMERICAL LINEAR ALGEBRA	535	(38)
9 Numerical Linear Algebra	535	(38)
9.1 Error Analysis	535	(3)
9.2 Linear Systems	538	(11)
9.3 LU-Factorization (Optional)	549	(7)
9.4 QR-Factorization (Optional)	556	(5)
9.5 Eigenvalues and Eigenvectors	561	(12)
Part IV MATLAB FOR LINEAR ALGEBRA	573
10 MATLAB for Linear Algebra	573
10.1 Input and Output in MATLAB	573	(6)
10.2 Matrix Operations in MATLAB	579	(3)
10.3 Matrix Powers and Some Special Matrices	582	(3)
10.4 Elementary Row Operations in MATLAB	585	(10)
10.5 Matrix Inverses in MATLAB	595	(1)
10.6 Vectors in MATLAB	596	(2)
10.7 Applications of Linear Combinations in MATLAB	598	(4)
10.8 Linear Transformations in MATLAB	602	(2)
10.9 MATLAB Command Summary	604
Appendix A Complex Numbers	A1
A.1 Complex Numbers	A1
A.2 Complex Numbers in Linear Algebra	A10
Appendix B Further Directions	A23
B.1 Inner Product Spaces (Calculus Required)	A23
B.2 Composite and Invertible Linear Transformations	A32
Answers to Odd-Numbered Exercises and Chapter Tests	A41
Index	I1