Linear Algebra with Applications

✍ Scribed by Jeffrey Holt

• Publisher: W. H. Freeman
• Year: 2012
• Tongue: English
• Leaves: 518
• Edition: First Edition
• Category: Library

✦ Synopsis

Holt's Linear Algebra with Applications blends computational and conceptual topics throughout. Early treatment of conceptual topics in the context of Euclidean space gives students more time, and a familiar setting, in which to absorb them. This organization also makes it possible to treat eigenvalues and eigenvectors earlier than in most texts. Abstract vector spaces are introduced later, once students have developed a solid conceptual foundation. Concepts and topics are frequently accompanied by applications to provide context and motivation. Because many students learn by example, Linear Algebra with Applications provides a large number of representative examples, over and above those used to introduce topics. The text also has over 2500 exercises, covering computational and conceptual topics over a range of difficulty levels.

✦ Table of Contents

Cover
......Page 1
Title Page......Page 3
Copyright
......Page 4
Dedication......Page 5
CONTENTS......Page 7
Preface......Page 9
1.1 Lines and Linear Equations......Page 19
1.2 Linear Systems and Matrices......Page 32
1.3 Numerical Solutions......Page 47
1.4 Applications of Linear Systems......Page 55
2.1 Vectors......Page 65
2.2 Span......Page 75
2.3 Linear Independence......Page 85
3.1 Linear Transformations......Page 99
3.2 Matrix Algebra......Page 113
3.3 Inverses......Page 131
3.4 LU Factorization......Page 145
3.5 Markov Chains......Page 159
4.1 Introduction to Subspaces......Page 169
4.2 Basis and Dimension......Page 178
4.3 Row and Column Spaces......Page 190
5.1 The Determinant Function......Page 199
5.2 Properties of the Determinant......Page 212
5.3 Applications of the Determinant......Page 222
6.1 Eigenvalues and Eigenvectors......Page 235
6.2 Approximation Methods......Page 248
6.3 Change of Basis......Page 257
6.4 Diagonalization......Page 267
6.5 Complex Eigenvalues......Page 277
6.6 Systems of Differential Equations......Page 286
7.1 Vector Spaces and Subspaces......Page 295
7.2 Span and Linear Independence......Page 304
7.3 Basis and Dimension......Page 312
8.1 Dot Products and Orthogonal Sets......Page 321
8.2 Projection and the Gram-Schmidt Process......Page 332
8.3 Diagonalizing Symmetric Matrices and QR Factorization......Page 342
8.4 The Singular Value Decomposition......Page 350
8.5 Least Squares Regression......Page 357
9.1 Definition and Properties......Page 367
9.2 Isomorphisms......Page 375
9.3 The Matrix of a Linear Transformation......Page 382
9.4 Similarity......Page 388
10.1 Inner Products......Page 397
10.2 The Gram–Schmidt Process Revisited......Page 406
10.3 Applications of Inner Products......Page 416
11.1 Quadratic Forms......Page 427
11.2 Positive Definite Matrices......Page 435
11.3 Constrained Optimization......Page 441
11.4 Complex Vector Spaces......Page 447
11.5 Hermitian Matrices......Page 453
Glossary......Page 461
Answers to Selected Exercises......Page 471
Index......Page 505