ISBN-10:
0471433276
ISBN-13:
9780471433279
Pub. Date:
12/09/2003
Publisher:
Wiley, John & Sons, Incorporated
Elementary Linear Algebra / Edition 8

Elementary Linear Algebra / Edition 8

by Howard A. Anton
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Overview

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.

Product Details

ISBN-13: 9780471433279
Publisher: Wiley, John & Sons, Incorporated
Publication date: 12/09/2003
Edition description: Older Edition
Pages: 608
Product dimensions: 8.28(w) x 10.38(h) x 1.52(d)

Table of Contents

Chapter 1Systems of Linear Equations and Matrices1
1.1Introduction to Systems of Linear Equations2
1.2Gaussian Elimination8
1.3Matrices and Matrix Operations23
1.4Inverses; Rules of Matrix Arithmetic39
1.5Elementary Matrices and a Method for Finding A[superscript -1]51
1.6Further Results on Systems of Equations and Invertibility60
1.7Diagonal, Triangular, and Symmetric Matrices68
Chapter 2Determinants83
2.1Determinants by Cofactor Expansion84
2.2Evaluating Determinants by Row Reduction96
2.3Properties of the Determinant Function103
2.4A Combinatorial Approach to Determinants111
Chapter 3Vectors in 2-Space and 3-Space123
3.1Introduction to Vectors (Geometric)124
3.2Norm of a Vector; Vector Arithmetic131
3.3Dot Product; Projections136
3.4Cross Product144
3.5Lines and Planes in 3-Space156
Chapter 4Euclidean Vector Spaces167
4.1Euclidean n-Space168
4.2Linear Transformations from R[superscript n] to R[superscript m]181
4.3Properties of Linear Transformations from R[superscript n] to R[superscript m]197
4.4Linear Transformations and Polynomials210
Chapter 5General Vector Spaces221
5.1Real Vector Spaces222
5.2Subspaces229
5.3Linear Independence240
5.4Basis and Dimension250
5.5Row Space, Column Space, and Nullspace266
5.6Rank and Nullity279
Chapter 6Inner Product Spaces295
6.1Inner Products296
6.2Angle and Orthogonality in Inner Product Spaces307
6.3Orthonormal Bases; Gram-Schmidt Prodcess; QR-Decomposition318
6.4Best Approximation; Least Squares332
6.5Change of Basis341
6.6Orthogonal Matrices347
Chapter 7Eigenvalues, Eigenvectors359
7.1Eigenvalues and Eigenvectors360
7.2Diagonalization369
7.3Orthogonal Diagonalization380
Chapter 8Linear Transformations389
8.1General Linear Transformations390
8.2Kernel and Range400
8.3Inverse Linear Transformations407
8.4Matrices of General Linear Transformations416
8.5Similarity430
8.6Isomorphism442
Chapter 9Additional Topics451
9.1Application to Differential Equations452
9.2Geometry of Linear Operators on R[superscript 2]458
9.3Least Squares Fitting to Data468
9.4Approximation Problems; Fourier Series474
9.5Quadratic Forms479
9.6Diagonalizing Quadratic Forms; Conic Sections487
9.7Quadric Surfaces497
9.8Comparison of Procedures for Solving Linear Systems502
9.9LU-Decompositions511
Chapter 10Complex Vector Spaces521
10.1Complex Numbers522
10.2Division of Complex Numbers528
10.3Polar Form of a Complex Number533
10.4Complex Vector Spaces540
10.5Complex Inner Product Spaces547
10.6Unitary Normal, and Hermitian Matrices554
Answers to Exercises567
Index599

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