Elementary Linear Algebra, 8th Edition

by Howard Anton (Drexel Univ.)

• ISBN13: 9780471170556
• ISBN10: 0471170550
• Edition: 8th
• Format: Hardcover
• Copyright: 2000-01-01
• Publisher: Wiley

Summary

A first course in linear algebra for mathematics, engineering and computer science students.Praised over many editions for its expository style and clarity of presentation, the revision of this best-selling text combines linear algebra theory with applications, and addresses a new generation of students' changing needs..This text can be used in a first or second year 1- or 2- semester course. Calculus is not a prerequisite, but there are exercises, examples, and applications for students with calculus backgrounds; they are clearly marked and can be omitted with no loss of continuity.

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 Independence	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)
Answers to Exercises	531	(48)
Photo Credits	579	(2)
Index	581