Linear Algebra with Applications

by Williams, Gareth

• ISBN13: 9780763732356
• ISBN10: 0763732354
• Edition: 5th
• Format: Hardcover
• Copyright: 2004-09-01
• Publisher: Jones & Bartlett

Summary

Linear Algebra with Applications, Fifth Edition is designed for an introductory course in linear algebra.

Table of Contents

Systems of Linear Equations	1	(42)
Matrices and Systems of Linear Equations	2	(14)
Gauss-Jordan Elimination	16	(12)
Curve Fitting, Electrical Networks, and Traffic Flow	28	(15)
Chapter 1 Review Exercises	39	(4)
Matrices	43	(88)
Addition, Scalar Multiplication, and Multiplication of Matrices	44	(17)
Algebraic Properties of Matrix Operations	61	(13)
Symmetric Matrices and Seriation in Archaeology	74	(12)
The Inverse of a Matrix and Cryptography	86	(16)
The Leontief Input-Output Model in Economics	102	(6)
Markov Chains, Population Movements, and Genetics	108	(9)
A Communication Model and Group Relationships in Sociology	117	(14)
Chapter 2 Review Exercises	128	(3)
Determinants	131	(36)
Introduction to Determinants	132	(9)
Properties of Determinants	141	(7)
Numerical Evaluation of a Determinant	148	(5)
Determinants, Matrix Inverses, and Systems of Linear Equations	153	(14)
Chapter 3 Review Exercises	161	(6)
Vector Spaces	167	(104)
The Vector Space Rn	168	(10)
Dot Product, Norm, Angle, and Distance	178	(15)
General Vector Spaces	193	(7)
Subspaces	200	(7)
Linear Combinations of Vectors	207	(14)
Linear Dependence and Independence	221	(7)
Basis and Dimension	228	(11)
Rank of a Matrix	239	(12)
Orthonormal Vectors and Projections in Rn	251	(20)
Chapter 4 Review Exercises	265	(6)
Eigenvalues and Eigenvectors	271	(42)
Eigenvalues and Eigenvectors	272	(7)
Demography and Weather Prediction	279	(7)
Diagonalization of Matrices	286	(11)
Quadratic Forms, Difference Equations, and Normal Modes	297	(16)
Chapter 5 Review Exercises	312	(1)
Linear Transformations	313	(78)
Introduction to Linear Transformations	314	(9)
Matrix Transformations, Computer Graphics, and Fractals	323	(21)
Kernel and Range	344	(12)
Transformations and Systems of Linear Equations	356	(9)
Coordinate Vectors	365	(10)
Matrix Representations of Linear Transformations	375	(16)
Chapter 6 Review Exercises	388	(3)
Inner Product Spaces	391	(40)
Inner Product Spaces	392	(10)
Non-Euclidean Geometry and Special Relativity	402	(7)
Approximation of Functions and Coding Theory	409	(8)
Least-Squares Curves	417	(14)
Chapter 7 Review Exercises	430	(1)
Numerical Techniques	431	(46)
Gaussian Elimination	432	(6)
The Method of LU Decomposition	438	(8)
Practical Difficulties in Solving systems of Equations	446	(11)
Iterative Methods for Solving Systems of Linear Equations	457	(6)
Eigenvalues by Iteration; Connectivity of Networks	463	(14)
Chapter 8 Review Exercises	475	(2)
Linear Programming	477	(26)
A Geometrical Introduction to Linear Programming	478	(9)
The Simplex Method	487	(7)
Geometrical Explanation of the Simplex Method	494	(9)
Chapter 9 Review Exercises	501	(2)
Appendix A Cross Product	503	(12)
Appendix B Equations of Planes and Lines in Three-Space	515	(8)
Appendix C Graphing Calculator Manual	523	(6)
C.1 Reduced Echelon Form of a Matrix (Sections 1.1, 1.2)	524	(1)
C.2 Matrix Operations (Sections 2.1, 2.2)	524	(1)
C.3 Powers of a Matrix (Section 2.2)	525	(1)
C.4 Transpose of a Matrix (Section 2.3)	525	(1)
C.5 Inverse of a Matrix (Section 2.4)	526	(1)
C.6 Determinant of a Matrix (Section 3.1)	526	(1)
C.7 Summary of Formats for Row Operations (Sections 1.1, 1.2)	527	(2)
Appendix D MATLAB Manual	529	(62)
D.1 Entering and Displaying a Matrix (Section 1.1)	530	(1)
D.2 Solving Systems of Linear Equations (Sections 1.1, 1.2, 1.3)	531	(4)
D.3 Matrix Operations, Submatrices, Rows and Columns (Sections 2.1, 2.2, 2.3)	535	(1)
D.4 Matrix Operations (Sections 2.1, 2.2, 2.3)	535	(4)
D.5 Computational Considerations (Section 2.2)	539	(1)
D.6 Inverse of a Matrix (Section 2.4)	540	(2)
D.7 Solving Systems of Equations Using Matrix Inverse (Section 2.4)	542	(3)
D.8 Cryptography (Section 2.4)	545	(1)
D.9 Leontief I/O Model (Section 2.5)	546	(2)
D.10 Markov Chains (Sections 2.6, 6.2)	548	(3)
D.11 Digraphs (Section 2.7)	551	(2)
D.12 Determinants (Sections 3.1, 3.2, 3.3)	553	(1)
D.13 Cramer's Rule (Section 3.4)	554	(3)
D.14 Linear Combinations, Linear Dependence, Basis (Sections 4.5-4.7)	557	(2)
D.15 Projection, Gram-Schmidt Orthogonalization (Section 4.8)	559	(5)
D.16 Eigenvalues and Eigenvectors and Applications (Sections 5.1-5.4)	564	(1)
D.17 Transformations Defined by Matrices (Sections 6.1, 6.2)	564	(1)
D.18 Fractals (Section 6.2)	565	(3)
D.19 Kernel and Range (Section 6.3)	568	(1)
D.20 Inner Product, Non-Euclidean Geometry (Sections 7.1, 7.2)	569	(3)
D.21 Space-Time Travel (Section 7.2)	572	(2)
D.22 Pseudoinverse and Least-Squares Curves (Section 7.4)	574	(4)
D.23 LU Decomposition (Section 8.2)	578	(3)
D.24 Condition Number of a Matrix (Section 8.3)	581	(2)
D.25 Jacobi and Gauss-Seidel Iterative Methods (Section 8.4)	583	(3)
D.26 The Simplex Method in Linear Programming (Section 9.2)
D.27 Cross Product (Appendix A)	586	(2)
D.28 MATLAB Commands, Functions, and M-files	588	(1)
D.29 Linear Algebra with Applications Toolbox M-files	588	(3)
Answers to Selected Exercises	591	(66)
Index	657