Elementary Linear Algebra: Applications Version, 7th Edition

by Howard Anton; Chris Rorres

• ISBN13: 9780471587415
• ISBN10: 0471587419
• Edition: 7th
• Format: Hardcover
• Copyright: 1994-05-01
• Publisher: Wiley

Summary

Noted for its expository style and clarity of presentation this substantial revision reflects a new generation of students2 changing needs. Proceeds from familiar concepts to the unfamiliar, from the concrete to the abstract. Features a wide variety of interesting contemporary applications which have been extensively revised and updated. Includes new material on least squares and QR-decomposition and greater emphasis on visualization.

Table of Contents

Systems of Linear Equations and Matrices	1	(78)
Introduction to Systems of Linear Equations	1	(7)
Gaussian Elimination	8	(17)
Matrices and Matrix Operations	25	(13)
Inverses; Rules of Matrix Arithmetic	38	(12)
Elementary Matrices and a Method for Finding A-1	50	(9)
Further Results on Systems of Equations and Invertibility	59	(7)
Diagonal, Triangular, and Symmetric Matrices	66	(13)
Determinants	79	(38)
The Determinant Function	79	(7)
Evaluating Determinants by Row Reduction	86	(6)
Properties of the Determinant Function	92	(9)
Cofactor Expansion; Cramer's Rule	101	(16)
Vectors in 2-Space and 3-Space	117	(50)
Introduction to Vectors (Geometric)	117	(10)
Norm of a Vector; Vector Arithmetic	127	(4)
Dot Product; Projections	131	(10)
Cross Product	141	(13)
Lines and Planes in 3-Space	154	(13)
Euclidean Vector Spaces	167	(48)
Euclidean n-Space	167	(14)
Linear Transformations from Rn to Rm	181	(18)
Properties of Linear Transformations from Rn to Rm	199	(16)
General Vector Spaces	215	(72)
Real Vector Spaces	215	(7)
Subspaces	222	(10)
Linear Independence	232	(9)
Basis and Dimension	241	(17)
Row Space, Column Space, and Nullspace	258	(14)
Rank and Nullity	272	(15)
Inner Product Spaces	287	(68)
Inner Products	287	(12)
Angle and Orthogonality in Inner Product Spaces	299	(13)
Orthonormal Bases; Gram-Schmidt Process; QR-Decomposition	312	(16)
Best Approximation; Least Squares	328	(10)
Orthogonal Matrices; Change of Basis	338	(17)
Eigenvalues, Eigenvectors	355	(28)
Eigenvalues and Eigenvectors	355	(10)
Diagonalization	365	(10)
Orthogonal Diagonalization	375	(8)
Linear Transformations	383	(58)
General Linear Transformations	383	(12)
Kernel and Range	395	(7)
Inverse Linear Transformations	402	(8)
Matrices of General Linear Transformations	410	(14)
Similarity	424	(17)
Additional Topics	441	(80)
Application to Differential Equations	441	(7)
Geometry of Linear Operators on R2	448	(12)
Least Squares Fitting to Data	460	(7)
Approximation Problems; Fourier Series	467	(7)
Quadratic Forms	474	(9)
Diagonalizing Quadratic Forms; Conic Sections	483	(12)
Quadric Surfaces	495	(5)
Comparison of Procedures for Solving Linear Systems	500	(10)
LU-Decompositions	510	(11)
Complex Vector Spaces	521	(50)
Complex Numbers	521	(7)
Modulus; Complex Conjugate; Division	528	(7)
Polar Form; DeMoivre's Theorem	535	(9)
Complex Vector Spaces	544	(7)
Complex Inner Product Spaces	551	(8)
Unitary, Normal, and Hermitian Matrices	559	(12)
Applications of Linear Algebra	571
Constructing Curves and Surfaces Through Specified Points	571	(6)
Electrical Networks	577	(3)
Geometric Linear Programming	580	(14)
The Assignment Problem	594	(9)
Cubic Spline Interpolation	603	(11)
Markov Chains	614	(11)
Graph Theory	625	(13)
Games of Strategy	638	(9)
Leontief Economic Models	647	(9)
Forest Management	656	(9)
Computer Graphics	665	(10)
Equilibrium Temperature Distributions	675	(10)
Computed Tomography	685	(14)
Fractals	699
Chaos	617	(15)
Cryptography	632	(112)
Genetics	744	(10)
Age-Specific Population Growth	754	(10)
Harvesting of Animal Populations	764	(9)
A Least Squares Model for Human Hearing	773
Answers to Exercises	A-1	(1)
Insert Photo Credits	P-1	(1)
Index	I-1