Linear Algebra with Applications (2-Download)

by Otto Bretscher

• ISBN13: 9780131907294
• ISBN10: 0131907298
• Format: Nonspecific Binding
• Copyright: 2013-06-21
• Publisher: PEARSO

Summary

Linear transformations and mappings are a running theme in this text. Geometric explication and history are heavily integrated. After the introduction of eigenvalues, dynamical systems becomes a running sub-theme. Has the finest collection of problems ever produced for this course.

Table of Contents

Preface	ix
1 Linear Equations	1	(51)
1.1 Introduction to Linear Systems	1	(11)
1.2 Matrices and Gauss-Jordan Elimination	12	(21)
1.3 On the Solutions of Linear Systems	33	(19)
2 Linear Transformations	52	(76)
2.1 Introduction to Linear Transformations and Their Inverses	52	(13)
2.2 Linear Transformations in Geometry	65	(21)
2.3 The Inverse of a Linear Transformation	86	(11)
2.4 Matrix Products	97	(31)
3 Subspaces of Rn and Their Dimensions	128	(49)
3.1 Image and Kernel of a Linear Transformation	128	(18)
3.2 Subspaces of Rn; Bases and Linear Independence	146	(14)
3.3 The Dimension of a Subspace of Rn	160	(17)
4 Orthogonality and Least Squares	177	(62)
4.1 Orthonormal Bases and Orthogonal Projections	177	(21)
4.2 Gram-Schmidt Process and QR Factorization	198	(9)
4.3 Orthogonal Transformations and Orthogonal Matrices	207	(11)
4.4 Least Squares and Data Fitting	218	(21)
5 Determinants	239	(52)
5.1 Introduction to Determinants	239	(11)
5.2 Properties of the Determinant	250	(22)
5.3 Geometrical Interpretations of the Determinant; Cramer's Rule	272	(19)
6 Eigenvalues and Eigenvectors	291	(80)
6.1 Dynamical Systems and Eigenvectors: An Introductory Example	291	(16)
6.2 Finding the Eigenvalues of a Matrix	307	(14)
6.3 Finding the Eigenvectors of a Matrix	321	(20)
6.4 Complex Eigenvalues	341	(16)
6.5 Stability	357	(14)
7 Coordinate Systems	371	(67)
7.1 Coordinate Systems in Rn	371	(16)
7.2 Diagonalization and Similarity	387	(14)
7.3 Symmetric Matrices	401	(12)
7.4 Quadratic Forms	413	(12)
7.5 Singular Values	425	(13)
8 Linear Systems of Differential Equations	438	(39)
8.1 An Introduction to Continuous Dynamical Systems	438	(20)
8.2 The Complex Case: Euler's Formula	458	(19)
9 Linear Spaces	477	(69)
9.1 An Introduction to Linear Spaces	477	(19)
9.2 Coordinates in a Linear Space	496	(15)
9.3 Inner Product Spaces	511	(17)
9.4 Linear Differential Operators	528	(18)
APPENDIX A Vectors	546
Answers to Odd-Numbered Exercises	A-1
Index	I-1