Linear Algebra and Its Applications (4th Edition)

Cover......Page 1
Linear Algebra and Its Applications (Fourth Edition)......Page 2
Contents......Page 3
Preface......Page 6
1.1 Introduction......Page 11
1.2 The Geometry of Linear Equations......Page 14
1.3 An Example of Gaussian Elimination......Page 23
1.4 Matrix Notation and Matrix Multiplication......Page 31
1.5 Triangular Factors and Row Exchanges......Page 46
1.6 Inverses and Transposes......Page 60
1.7 Special Matrices and Applications......Page 76
Review Exercises......Page 82
2.1 Vector Spaces and Subspaces......Page 87
2.2 Solving Ax = 0 and Ax = b......Page 96
2.3 Linear Independence, Basis, and Dimension......Page 113
2.4 The Four Fundamental Subspaces......Page 125
2.5 Graphs and Networks......Page 139
2.6 Linear Transformations......Page 150
Review Exercises......Page 164
3.1 Orthogonal Vectors and Subspaces......Page 169
3.2 Cosines and Projections onto Lines......Page 181
3.3 Projections and Least Squares......Page 190
3.4 Orthogonal Bases and Gram-Schmidt......Page 205
3.5 The Fast Fourier Transform......Page 221
Review Exercises......Page 231
4.1 Introduction......Page 235
4.2 Properties of the Determinant......Page 237
4.3 Formulas for the Determinant......Page 246
4.4 Applications of Determinants......Page 257
Review Exercises......Page 268
5.1 Introduction......Page 270
5.2 Diagonalization of a Matrix......Page 283
5.3 Difference Equations and Powers A^k......Page 293
5.4 Differential Equations and e^{At}......Page 306
5.5 Complex Matrices......Page 322
5.6 Similarity Transformations......Page 335
Review Exercises......Page 351
6.1 Minima, Maxima, and Saddle Points......Page 355
6.2 Tests for Positive Definiteness......Page 362
6.3 Singular Value Decomposition......Page 377
6.4 Minimum Principles......Page 386
6.5 The Finite Element Method......Page 394
7.1 Introduction......Page 400
7.2 Matrix Norm and Condition Number......Page 401
7.3 Computation of Eigenvalues......Page 409
7.4 Iterative Methods for Ax = b......Page 417
8.1 Linear Inequalities......Page 427
8.2 The Simplex Method......Page 432
8.3 The Dual Problem......Page 444
8.4 Network Models......Page 454
8.5 Game Theory......Page 461
A.1 The Intersection of Two Vector Spaces......Page 469
A.2 The Sum of Two Vector Spaces......Page 470
A.4 The Tensor Product of Two Vector Spaces......Page 471
A.5 The Kronecker Product A⊗B of Two Matrices......Page 472
B The Jordan Form......Page 476
C Matrix Factorizations......Page 483
D Glossary: A Dictionary for Linear Algebra......Page 485
E MATLAB Teaching Codes......Page 494
F Linear Algebra in a Nutshell......Page 496
Problem Set 1.3......Page 497
Problem Set 1.4......Page 498
Problem Set 1.5......Page 500
Problem Set 1.6......Page 502
Problem Set 2.1......Page 505
Problem Set 2.2......Page 506
Problem Set 2.3......Page 509
Problem Set 2.4......Page 511
Problem Set 2.5......Page 512
Problem Set 2.6......Page 513
Problem Set 3.1......Page 515
Problem Set 3.2......Page 516
Problem Set 3.3......Page 517
Problem Set 3.4......Page 518
Problem Set 3.5......Page 519
Problem Set 4.2......Page 520
Problem Set 4.3......Page 521
Problem Set 4.4......Page 523
Problem Set 5.1......Page 524
Problem Set 5.2......Page 525
Problem Set 5.3......Page 527
Problem Set 5.4......Page 528
Problem Set 5.5......Page 529
Problem Set 5.6......Page 531
Problem Set 6.1......Page 532
Problem Set 6.2......Page 533
Problem Set 6.3......Page 535
Problem Set 6.5......Page 536
Problem Set 7.2......Page 537
Problem Set 7.4......Page 538
Problem Set 8.1......Page 539
Problem Set 8.3......Page 540
Problem Set 8.5......Page 541
Problem Set B......Page 542