Introductory Linear Algebra : An Applied First Course

by Kolman, Bernard; Hill, David R.

• ISBN13: 9780131437401
• ISBN10: 0131437402
• Additional ISBN(s): 9780130182654
• Edition: 8th
• Format: Hardcover
• Copyright: 2005-01-01
• Publisher: Prentice Hall
• More Book Details
• Purchase Benefits

Summary

This book presents an introduction to linear algebra and to some of its significant applications. It covers the essentials of linear algebra (including Eigenvalues and Eigenvectors) and shows how the computer is used for applications.Emphasizing the computational and geometrical aspects of the subject, this popular book covers the following topics comprehensively but not exhaustively: linear equations and matrices and their applications; determinants; vectors and linear transformations; real vector spaces; eigenvalues, eigenvectors, and diagonalization; linear programming; and MATLAB for linear algebra.Its useful and comprehensive appendices make this an excellent desk reference for anyone involved in mathematics and computer applications.

Table of Contents

Preface	xi
To the Student	xix
Linear Equations and Matrices	1	(118)
Linear Systems	1	(9)
Matrices	10	(11)
Dot Product and Matrix Multiplication	21	(18)
Properties of Matrix Operations	39	(13)
Matrix Transformations	52	(10)
Solutions of Linear Systems of Equations	62	(29)
The Inverse of a Matrix	91	(16)
LU-Factorization (Optional)	107	(12)
Applications of Linear Equations and Matrices (Optional)	119	(63)
An Introduction to Coding	119	(6)
Graph Theory	125	(10)
Computer Graphics	135	(9)
Electrical Circuits	144	(5)
Markov Chains	149	(10)
Linear Economic Models	159	(7)
Introduction to Wavelets	166	(16)
Determinants	182	(32)
Definition and Properties	182	(14)
Cofactor Expansion and Applications	196	(14)
Determinants from a Computational Point of View	210	(4)
Vectors in Rn	214	(45)
Vectors in the Plane	214	(15)
n-Vectors	229	(18)
Linear Transformations	247	(12)
Applications of Vectors in R2 and R3 (Optional)	259	(13)
Cross Product in R3	259	(5)
Lines and Planes	264	(8)
Real Vector Spaces	272	(103)
Vector Spaces	272	(7)
Subspaces	279	(12)
Linear Independence	291	(12)
Basis and Dimension	303	(14)
Homogeneous Systems	317	(11)
The Rank of a Matrix and Applications	328	(12)
Coordinates and Change of Basis	340	(12)
Orthonormal Bases in Rn	352	(8)
Orthogonal Complements	360	(15)
Applications of Real Vector Spaces (Optional)	375	(33)
QR-Factorization	375	(3)
Least Squares	378	(12)
More on Coding	390	(18)
Eigenvalues, Eigenvectors, and Diagonalization	408	(39)
Eigenvalues and Eigenvectors	408	(14)
Diagonalization	422	(11)
Diagonalization of Symmetric Matrices	433	(14)
Applications of Eigenvalues and Eigenvectors (Optional)	447	(55)
The Fibonacci Sequence	447	(4)
Differential Equations (Calculus Required)	451	(10)
Dynamical Systems (Calculus Required)	461	(14)
Quadratic Forms	475	(9)
Conic Sections	484	(7)
Quadric Surfaces	491	(11)
Linear Transformations and Matrices	502	(53)
Definition and Examples	502	(6)
The Kernel and Range of a Linear Transformation	508	(13)
The Matrix of a Linear Transformation	521	(15)
Introduction to Fractals (Optional)	536	(19)
Cumulative Review of Introductory Linear Algebra	555	(3)
Linear Programming (Optional)	558	(57)
The Linear Programming Problem; Geometric Solution	558	(17)
The Simplex Method	575	(16)
Duality	591	(7)
The Theory of Games	598	(17)
Matlab for Linear Algebra	615	(1)
Input and Output in Matlab	616	(4)
Matrix Operations in Matlab	620	(3)
Matrix Powers and Some Special Matrices	623	(2)
Elementary Row Operations in Matlab	625	(9)
Matrix Inverses in Matlab	634	(1)
Vectors in Matlab	635	(2)
Applications of Linear Combinations in Matlab	637	(3)
Linear Transformations in Matlab	640	(3)
Matlab Command Summary	643
APPENDIX A Complex Numbers	1	(18)
A.1 Complex Numbers	1	(8)
A.2 Complex Numbers in Linear Algebra	9	(10)
APPENDIX B Further Directions	19	(20)
B.1 Inner Product Spaces (Calculus Required)	19	(11)
B.2 Composite and Invertible Linear Transformations	30	(9)
Glossary for Linear Algebra	39	(6)
Answers to Odd-Numbered Exercises and Chapter Tests	45
Index	1