Elementary Linear Algebra, Applications Version, 8th Edition,9780471170525

Elementary Linear Algebra, Applications Version, 8th Edition

by ;
Edition: 8th
ISBN13: 9780471170525
ISBN10: 0471170526
Format: Hardcover
Pub. Date: 2000-01-01
Publisher(s): Wiley
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List Price: $144.85

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Summary

This classic treatment of linear algebra presents the fundamentals in the clearest possible way, examining basic ideas by means of computational examples and geometrical interpretation. It proceeds from familiar concepts to the unfamiliar, from the concrete to the abstract. Readers consistently praise this outstanding text for its expository style and clarity of presentation.

Table of Contents

Systems of Linear Equations and Matrices
1(81)
Introduction to Systems of Linear Equations
2(6)
Gaussian Elimination
8(15)
Matrices and Matrix Operations
23(14)
Inverses; Rules of Matrix Arithmetic
37(13)
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(15)
Determinants
81(38)
The Determinant Function
82(7)
Evaluating Determinants by Row Reduction
89(6)
Properties of the Determinant Function
95(9)
Cofactor Expansion; Cramer's Rule
104(15)
Vectors in 2-Space and 3-Space
119(42)
Introduction to Vectors (Geometric)
120(6)
Norm of a Vector; Vector Arithmetic
126(4)
Dot Product; Projections
130(8)
Cross Product
138(11)
Lines and Planes in 3-Space
149(12)
Euclidean Vector Spaces
161(42)
Euclidean n-Space
162(11)
Linear Transformations from Rn to Rm
173(16)
Properties of Linear Transformations from Rn to Rm
189(14)
General Vector Spaces
203(72)
Real Vector Spaces
204(7)
Subspaces
211(10)
Linear Indepencence
221(10)
Basis and Dimension
231(15)
Row Space, Column Space, and Nullspace
246(13)
Rank and Nullity
259(16)
Inner Product Spaces
275(62)
Inner Products
276(11)
Angle and Orthogonality in Inner Product Spaces
287(11)
Orthonormal Bases; Gram-Schmidt Process; QR-Decomposition
298(13)
Best Approximation; Least Squares
311(9)
Orthogonal Matrices; Change of Basis
320(17)
Eigenvalues, Eigenvectors
337(28)
Eigenvalues and Eigenvectors
338(9)
Diagonalization
347(10)
Orthogonal Diagonalization
357(8)
Linear Transformations
365(54)
General Linear Transformations
366(10)
Kernel and Range
376(6)
Inverse Linear Transformations
382(8)
Matrices of General Linear Transformations
390(12)
Similarity
402(17)
Additional Topics
419(68)
Application to Differential Equations
420(6)
Geometry of Linear Operators on R2
426(11)
Least Squares Fitting to Data
437(5)
Approximation Problems; Fourier Series
442(5)
Quadratic Forms
447(7)
Diagonalizing Quadratic Forms; Conic Sections
454(9)
Quadric Surfaces
463(5)
Comparison of Procedures for Solving Linear Systems
468(9)
LU-Decompositions
477(10)
Complex Vector Spaces
487(44)
Complex Numbers
488(6)
Division of Complex Numbers
494(6)
Polar Form of a Complex Number
500(6)
Complex Vector Spaces
506(7)
Complex Inner Product Spaces
513(7)
Unitary, Normal, and Hermitian Matrices
520(11)
Applications of Linear Algebra
531(222)
Constructing Curves and Surfaces Through Specified Points
532(6)
Electrical Networks
538(4)
Geometric Linear Programming
542(12)
The Assignment Problem
554(11)
Cubic Spline Interpolation
565(11)
Markov Chains
576(11)
Graph Theory
587(11)
Games of Strategy
598(10)
Leontief Economic Models
608(10)
Forest Management
618(8)
Computer Graphics
626(10)
Equilibrium Temperature Distributions
636(11)
Computed Tomography
647(12)
Fractals
659(19)
Chaos
678(14)
Cryptography
692(13)
Genetics
705(11)
Age-Specific Population Growth
716(11)
Harvesting of Animal Populations
727(8)
A Least Squares Model for Human Hearing
735(7)
Warps and Morphs
742(11)
Answers To Exercises 753(58)
Photo Credits 811(2)
Index 813

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