Introductory Linear Algebra : An Applied First Course,9780131437401

Introductory Linear Algebra : An Applied First Course

by ;
Edition: 8th
ISBN13: 9780131437401
ISBN10: 0131437402
Format: Hardcover
Pub. Date: 2005-01-01
Publisher(s): Prentice Hall
List Price: $154.08

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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

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