Elementary Linear Algebra

by Kolman, Bernard; Hill, David R.

• ISBN13: 9780130851994
• ISBN10: 013085199X
• Edition: 7th
• Format: Hardcover
• Copyright: 1999-09-01
• Publisher: Pearson College Div

Summary

For first courses in Linear Algebra or Matrix Theory. This introductory text offers a fine balance between abstraction/theory and computational skills. While vector spaces come early, this is not a heavy duty theory text. This edition is more applied than ever before.

Table of Contents

Preface	xi
Linear Equations and Matrices	1	(83)
Systems of Linear Equations	1	(7)
Matrices; Matrix Operations	8	(12)
Algebraic Properties of Matrix Operations	20	(9)
Special Types of Matrices and Partitioned Matrices	29	(11)
Echelon Form of a Matrix	40	(20)
Elementary Matrices; Finding A--1	60	(9)
Equivalent Matrices	69	(4)
LU-Factorization (Optional)	73	(11)
Supplementary Exercises	81	(3)
Real Vector Spaces	84	(98)
Vectors in the Plane and in 3-Space	84	(12)
Vector Spaces	96	(7)
Subspaces	103	(11)
Span and Linear Independence	114	(11)
Basis and Dimension	125	(15)
Homogeneous Systems	140	(8)
Coordinates and Isomorphisms	148	(16)
Rank of a Matrix	164	(18)
Supplementary Exercises	178	(4)
Inner Product Spaces	182	(71)
Standard Inner Product on R2 and R3	182	(10)
Cross Product in R3 (Optional)	192	(7)
Inner Product Spaces	199	(14)
Gram-Schmidt Process	213	(13)
Orthogonal Complements	226	(17)
Least Squares (Optional)	243	(10)
Supplementary Exercises	250	(3)
Linear Transformations and Matrices	253	(62)
Definition and Examples	253	(12)
Kernel and Range of a Linear Transformation	265	(16)
Matrix of a Linear Transformation	281	(10)
Vector Space of Matrices and Vector Space of Linear Transformations (Optional)	291	(8)
Similarity	299	(7)
Computer Graphics (Optional)	306	(9)
Supplementary Exercises	312	(3)
Determinants	315	(36)
Definition	315	(5)
Properties of Determinants	320	(11)
Cofactor Expansion	331	(7)
Inverse of a Matrix	338	(5)
Other Applications of Determinants	343	(6)
Determinants from a Computational Point of View	349	(2)
Supplementary Exercises	350	(1)
Eigenvalues and Eigenvectors	351	(85)
Eigenvalues and Eigenvectors	351	(14)
Diagonalization and Similar Matrices	365	(10)
Stable Age Distribution in a Population; Markov Processes (Optional)	375	(7)
Diagonalization of Symmetric Matrices	382	(13)
Spectral Decomposition and Singular Value Decomposition (Optional)	395	(10)
Real Quadratic Forms	405	(10)
Conic Sections	415	(9)
Quadric Surfaces	424	(12)
Supplementary Exercises	435	(1)
Differential Equations (Optional)	436	(21)
Differential Equations	436	(11)
Dynamical Systems	447	(10)
Supplementary Exercises	455	(2)
MATLAB for Linear Algebra	457	(34)
Input and Output in MATLAB	458	(4)
Matrix Operations in MATLAB	462	(3)
Matrix Powers and Some Special Matrices	465	(3)
Elementary Row Operations in MATLAB	468	(10)
Matrix Inverses in MATLAB	478	(1)
Vectors in MATLAB	479	(2)
Applications of Linear Combinations in MATLAB	481	(4)
Linear Transformations in MATLAB	485	(2)
MATLAB Command Summary	487	(4)
MATLAB Exercises	491	(18)
Appendix A: Preliminaries	509	(4)
A.1 Sets	509	(1)
A.2 Functions	509	(4)
Appendix B: Complex Numbers	513	(22)
B.1 Complex Numbers	513	(9)
B.2 Complex Numbers in Linear Algebra	522	(13)
Answers to Odd-Numbered Exercises	535	(26)
Index	561