Linear Algebra With Applications

by Bretscher, Otto

• ISBN13: 9780130198570
• ISBN10: 0130198579
• Edition: 2nd
• Format: Hardcover
• Copyright: 2001-01-01
• Publisher: PRENTICE HALL

Summary

For courses in Introductory Linear Algebra and Matrix Methods. With the most geometric presentation now available, this text emphasizes linear transformations as a unifying theme, and enables students to "do" both computational and abstract math in each chapter. A second theme is introduced half way through the text when eigenvectors are reached on dynamical systems. It also includes a wider range of problem sets than found in any other text in this market.

Table of Contents

Preface	xi
Linear Equations	1	(38)
Introduction to Linear Systems	1	(8)
Matrices and Gauss-Jordan Elimination	9	(15)
On the Solutions of Linear Systems	24	(15)
Linear Transformations	39	(57)
Introduction to Linear Transformations and Their Inverses	39	(10)
Linear Transformations in Geometry	49	(16)
The Inverse of a Linear Transformation	65	(9)
Matrix Products	74	(22)
Subspaces of Rn and Their Dimensions	96	(52)
Image and Kernel of a Linear Transformation	96	(14)
Subspaces of Rn; Bases and Linear Independence	110	(11)
The Dimension of a Subspace of Rn	121	(13)
Coordinates	134	(14)
Linear Spaces	148	(29)
Introduction to Linear Spaces	148	(11)
Linear Transformations and Isomorphisms	159	(6)
Coordinates in a Linear Space	165	(12)
Orthogonality and Least Squares	177	(65)
Orthonormal Bases and Orthogonal Projections	177	(17)
Gram-Schmidt Process and QR Factorization	194	(7)
Orthogonal Transformations and Orthogonal Matrices	201	(10)
Least Squares and Data Fitting	211	(14)
Inner Product Spaces	225	(17)
Determinants	242	(46)
Introduction to Determinants	242	(9)
Properties of the Determinant	251	(18)
Geometrical Interpretations of the Determinant; Cramer's Rule	269	(19)
Eigenvalues and Eigenvectors	288	(77)
Dynamical Systems and Eigenvectors: An Introductory Example	288	(14)
Finding the Eigenvalues of a Matrix	302	(11)
Finding the Eigenvectors of a Matrix	313	(16)
Diagonalization	329	(10)
Complex Eigenvalues	339	(16)
Stability	355	(10)
Symmetric Matrices and Quadratic Forms	365	(31)
Symmetric Matrices	365	(9)
Quadratic Forms	374	(9)
Singular Values	383	(13)
Linear Differential Equations	396	(45)
An Introduction to Continuous Dynamical Systems	396	(15)
The Complex Case: Euler's Formula	411	(14)
Linear Differential Operators and Linear Differential Equations	425	(16)
Appendix A Vectors	441	(9)
Answers to Odd-Numbered Exercises	450	(22)
Subject Index	472	(6)
Name Index	478