Elementary Linear Algebra: Applications Version, 7th Edition,9780471587415

Elementary Linear Algebra: Applications Version, 7th Edition

by ;
Edition: 7th
ISBN13: 9780471587415
ISBN10: 0471587419
Format: Hardcover
Pub. Date: 1994-05-01
Publisher(s): Wiley
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List Price: $106.35

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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

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