Linear Algebra and Its Applications (4th Edition)

Renowned professor and author Gilbert Strang demonstrates that linear algebra is a fascinating subject by showing both its beauty and value. While the mathematics is there, the effort is not all concentrated on proofs. Strang's emphasis is on understanding. He explains concepts, rather than deduces. This book is written in an informal and personal style and teaches real mathematics. The gears change in Chapter 2 as students reach the introduction of vector spaces. Throughout the book, the theory is motivated and reinforced by genuine applications, allowing pure mathematicians to teach applied mathematics. 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 "Renowned professor and author Gilbert Strang demonstrates that linear algebra is a fascinating subject by showing both its beauty and value. While the mathematics is there, the effort is not all concentrated on proofs. Strang's emphasis is on understanding. He explains concepts, rather than deduces. This book is written in an informal and personal style and teaches real mathematics. The gears change in Chapter 2 as students reach the introduction of vector spaces. Throughout the book, the theory is motivated and reinforced by genuine applications, allowing pure mathematicians to teach applied mathematics."-- Amazon.com Demonstrates that linear algebra is a fascinating subject by showing both its beauty and value. Emphasizing on understanding, this book provides an introduction to vector spaces. The theory is motivated and reinforced by genuine applications, allowing pure mathematicians to teach applied mathematics. This text combines the underlying theory discussions with examples from electrical engineering, computer science, physics, biology, and economics. Demonstrates that linear algebra is a fascinating subject by showing both its beauty and value. This book explains concepts, rather than deduces.