Elementary Linear Algebra, 9th Edition

by Howard Anton (Drexel Univ.)

• ISBN13: 9780471669609
• ISBN10: 0471669601
• Edition: 9
• Format: Hardcover
• Copyright: 2004-12-01
• Publisher: WILEY

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. Clear, accessible, step-by-step explanations make the material crystal clear. The authors spotlight the relationships between concepts to give a unified and complete picture. Established the intricate thread of relationships between systems of equations, matrices, determinants, vectors, linear transformations and eigenvalues.

Table of Contents

Systems of Linear Equations and Matrices	1	(82)
Introduction to Systems of Linear Equations	2	(6)
Gaussian Elimination	8	(15)
Matrices and Matrix Operations	23	(16)
Inverses; Rules of Matrix Arithmetic	39	(12)
Elementary Matrices and a Method for Finding A-1	51	(9)
Further Results on Systems of Equations and Invertibility	60	(8)
Diagonal, Triangular, and Symmetric Matrices	68	(15)
Determinants	83	(40)
Determinants by Cofactor Expansion	84	(12)
Evaluating Determinants by Row Reduction	96	(7)
Properties of the Determinant Function	103	(8)
A Combinatorial Approach to Determinants	111	(12)
Vectors in 2-Space and 3-Space	123	(44)
Introduction to Vectors (Geometric)	124	(7)
Norm of a Vector; Vector Arithmetic	131	(5)
Dot Product; Projections	136	(8)
Cross Product	144	(12)
Lines and Planes in 3-Space	156	(11)
Euclidean Vector Spaces	167	(54)
Euclidean n-Space	168	(13)
Linear Transformations from Rn to Rm	181	(16)
Properties of Linear Transformations from Rn to Rm	197	(13)
Linear Transformations and Polynomials	210	(11)
General Vector Spaces	221	(74)
Real Vector Spaces	222	(7)
Subspaces	229	(11)
Linear Independence	240	(10)
Basis and Dimension	250	(16)
Row Space, Column Space, and Nullspace	266	(13)
Rank and Nullity	279	(16)
Inner Product Spaces	295	(64)
Inner Products	296	(11)
Angle and Orthogonality in Inner Product Spaces	307	(11)
Orthonormal Bases; Gram--Schmidt Prodcess; Q R-Decomposition	318	(14)
Best Approximation; Least Squares	332	(9)
Change of Basis	341	(6)
Orthogonal Matrices	347	(12)
Eigenvalues, Eigenvectors	359	(30)
Eigenvalues and Eigenvectors	360	(9)
Diagonalization	369	(11)
Orthogonal Diagonalization	380	(9)
Linear Transformations	389	(62)
General Linear Transformations	390	(10)
Kernel and Range	400	(7)
Inverse Linear Transformations	407	(9)
Matrices of General Linear Transformations	416	(14)
Similarity	430	(12)
Isomorphism	442	(9)
Additional Topics	451	(70)
Application to Differential Equations	452	(6)
Geometry of Linear Operators on R2	458	(10)
Least Squares Fitting to Data	468	(6)
Approximation Problems; Fourier Series	474	(5)
Quadratic Forms	479	(8)
Diagonalizing Quadratic Forms; Conic Sections	487	(10)
Quadric Surfaces	497	(5)
Comparison of Procedures for Solving Linear Systems	502	(9)
LU-Decompositions	511	(10)
Complex Vector Spaces	521	(46)
Complex Numbers	522	(6)
Division of Complex Numbers	528	(5)
Polar Form of a Complex Number	533	(7)
Complex Vector Spaces	540	(7)
Complex Inner Product Spaces	547	(7)
Unitary Normal, and Hermitian Matrices	554	(13)
Answers to Exercises	567	(32)
Index	599