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دسته بندی: ریاضیات کاربردی ویرایش: 4th نویسندگان: Gilbert Strang سری: ISBN (شابک) : 9780030105678, 8131501728 ناشر: سال نشر: 2005 تعداد صفحات: 508 زبان: English فرمت فایل : DJVU (درصورت درخواست کاربر به PDF، EPUB یا AZW3 تبدیل می شود) حجم فایل: 11 مگابایت
در صورت تبدیل فایل کتاب Linear Algebra and Its Applications, Fourth Edition به فرمت های PDF، EPUB، AZW3، MOBI و یا DJVU می توانید به پشتیبان اطلاع دهید تا فایل مورد نظر را تبدیل نمایند.
توجه داشته باشید کتاب جبر خطی و برنامه های کاربردی آن، نسخه چهارم نسخه زبان اصلی می باشد و کتاب ترجمه شده به فارسی نمی باشد. وبسایت اینترنشنال لایبرری ارائه دهنده کتاب های زبان اصلی می باشد و هیچ گونه کتاب ترجمه شده یا نوشته شده به فارسی را ارائه نمی دهد.
Gilbert Strang : Linear Algebra and It _Applications 4ed ... 1 Contents ... 3 Preface ... 6 Chapter 1 Matrices and Gaussian Elimination ... 11 1.1 Introduction ... 11 1.2 The Geometry of Linear Equations ... 14 Column Vectors and Linear Combinations ... 16 The Singular Case ... 18 1.3 An Example of Gaussian Elimination ... 23 The Breakdown of Elimination ... 24 The Cost of Elimination ... 25 1.4 Matrix Notation and Matrix Multiplication ... 31 Multiplication of a Matrix and a Vector ... 32 The Matrix Form of One Elimination Step ... 34 Matrix Multiplication ... 35 1.5 Triangular Factors and Row Exchanges ... 46 One Linear System = Two Triangular Systems ... 50 Row Exchanges and Permutation Matrices ... 51 Elimination in a Nutshell: PA = LU ... 53 1.6 Inverses and Transposes ... 60 The Calculation of A^?1: The Gauss-Jordan Method ... 62 Invertible = Nonsingular (n pivots) ... 64 The Transpose Matrix ... 65 Symmetric Matrices ... 66 Symmetric Products R^TR, RR^T, and LDL^T ... 67 1.7 Special Matrices and Applications ... 76 Roundoff Error ... 79 Review Exercises ... 82 Chapter 2 Vector Spaces ... 87 2.1 Vector Spaces and Subspaces ... 87 The Column Space of A ... 89 The Nullspace of A ... 91 2.2 Solving Ax = 0 and Ax = b ... 96 Echelon Form U and Row Reduced Form R ... 97 Pivot Variables and Free Variables ... 99 Solving Ax = b, Ux = c, and Rx = d ... 101 Another Worked Example ... 104 2.3 Linear Independence, Basis, and Dimension ... 113 Spanning a Subspace ... 116 Basis for a Vector Space ... 117 Dimension of a Vector Space ... 118 2.4 The Four Fundamental Subspaces ... 125 Existence of Inverses ... 131 Matrices of Rank 1 ... 133 2.5 Graphs and Networks ... 139 Spanning Trees and Independent Rows ... 142 The Ranking of Football Teams ... 143 Networks and Discrete Applied Mathematics ... 145 2.6 Linear Transformations ... 150 Transformations Represented by Matrices ... 153 Rotations Q, Projections P, and Re?ections H ... 156 Review Exercises ... 164 Chapter 3 Orthogonality ... 169 3.1 Orthogonal Vectors and Subspaces ... 169 Orthogonal Vectors ... 170 Orthogonal Subspaces ... 172 The Matrix and the Subspaces ... 175 3.2 Cosines and Projections onto Lines ... 181 inner products and cosines ... 182 Projection onto a Line ... 183 Projection Matrix of Rank 1 ... 185 Transposes from Inner Products ... 186 3.3 Projections and Least Squares ... 190 Least Squares Problems with Several Variables ... 191 The Cross-Product Matrix A^TA ... 193 Projection Matrices ... 194 Least-Squares Fitting of Data ... 195 Weighted Least Squares ... 198 3.4 Orthogonal Bases and Gram-Schmidt ... 205 Orthogonal Matrices ... 206 Rectangular Matrices with Orthogonal Columns ... 208 The Gram-Schmidt Process ... 211 The Factorization A = QR ... 213 Function Spaces and Fourier Series ... 214 3.5 The Fast Fourier Transform ... 221 Complex Roots of Unity ... 222 The Fourier Matrix and Its Inverse ... 224 The Fast Fourier Transform ... 226 The Complete FFT and the Butter?y ... 228 Review Exercises ... 231 Chapter 4 Determinants ... 235 4.1 Introduction ... 235 4.2 Properties of the Determinant ... 237 4.3 Formulas for the Determinant ... 246 Expansion of detA in Cofactors ... 249 4.4 Applications of Determinants ... 257 Review Exercises ... 268 Chapter 5 Eigenvalues and Eigenvectors ... 270 5.1 Introduction ... 270 The Solution of Ax =?x ... 272 Summary and Examples ... 274 Eigshow ... 277 5.2 Diagonalization of a Matrix ... 283 Examples of Diagonalization ... 285 Powers and Products: A^k and AB ... 286 5.3 Difference Equations and Powers A^k ... 293 Fibonacci Numbers ... 293 Markov Matrices ... 296 Stability of uk+1 = Auk ... 298 Positive Matrices and Applications in Economics ... 299 5.4 Differential Equations and e^At ... 306 stability of differential equations ... 310 Second-Order Equations ... 314 5.5 Complex Matrices ... 322 Complex Numbers and Their Conjugates ... 322 Lengths and Transposes in the Complex Case ... 324 Hermitian Matrices ... 325 Unitary Matrices ... 328 5.6 Similarity Transformations ... 335 Change of Basis = Similarity Transformation ... 337 Triangular Forms with a Unitary M ... 339 Diagonalizing Symmetric and Hermitian Matrices ... 340 The Jordan Form ... 342 Review Exercises ... 351 Chapter 6 Positive De?nite Matrices ... 355 6.1 Minima, Maxima, and Saddle Points ... 355 De?nite versus Inde?nite: Bowl versus Saddle ... 357 Higher Dimensions: Linear Algebra ... 358 6.2 Tests for Positive De?niteness ... 362 Positive De?nite Matrices and Least Squares ... 365 Semide?nite Matrices ... 365 Ellipsoids in n Dimensions ... 367 The Law of Inertia ... 369 The Generalized Eigenvalue Problem ... 370 6.3 Singular Value Decomposition ... 377 Application of the SVD ... 378 6.4 Minimum Principles ... 386 Minimizing with Constraints ... 387 Least Squares Again ... 389 The Rayleigh quotient ... 389 Intertwining of the Eigenvalues ... 390 6.5 The Finite Element Method ... 394 Trial Functions ... 395 Linear Finite Elements ... 396 Eigenvalue Problems ... 397 Chapter 7 Computations with Matrices ... 400 7.1 Introduction ... 400 7.2 Matrix Norm and Condition Number ... 401 Unsymmetric Matrices ... 403 A Formula for the Norm ... 405 7.3 Computation of Eigenvalues ... 409 Tridiagonal and Hessenberg Forms ... 411 The QR Algorithm for Computing Eigenvalues ... 414 7.4 Iterative Methods for Ax = b ... 417 Chapter 8 Linear Programming and Game Theory ... 427 8.1 Linear Inequalities ... 427 The Feasible Set and the Cost Function ... 428 Slack Variables ... 430 The Diet Problem and Its Dual ... 430 Typical Applications ... 431 8.2 The Simplex Method ... 432 The Geometry: Movement Along Edges ... 433 The Simplex Algorithm ... 435 The Tableau ... 437 The Organization of a Simplex Step ... 439 Karmarkar’s Method ... 441 8.3 The Dual Problem ... 444 The Proof of Duality ... 447 Shadow Prices ... 448 Interior Point Methods ... 449 The Theory of Inequalities ... 450 8.4 Network Models ... 454 The Marriage Problem ... 456 Spanning Trees and the Greedy Algorithm ... 458 Further Network Models ... 459 8.5 Game Theory ... 461 Matrix Games ... 463 The Minimax Theorem ... 464 Real Games ... 465 Appendix A Intersection, Sum, and Product of Spaces ... 469 A.1 The Intersection of Two Vector Spaces ... 469 A.2 The Sum of Two Vector Spaces ... 470 A.3 The Cartesian Product of Two Vector Spaces ... 471 A.4 The Tensor Product of Two Vector Spaces ... 471 A.5 The Kronecker Product A?B of Two Matrices ... 472 Problem Set A ... 474 Appendix B The Jordan Form ... 476 Appendix C Matrix Factorizations ... 483 Appendix D Glossary: A Dictionary for Linear Algebra ... 485 Appendix E MATLAB Teaching Codes ... 494 Solutions to Selected Exercises ... 497 Problem Set 1.2, page 9 ... 497 Problem Set 1.4, page 26 ... 498 Problem Set 1.5 page 39 ... 500 Problem Set 1.6, page 52 ... 502 Problem Set 1.7, page 63 ... 505 Problem Set 2.1, page 73 ... 505 Problem Set 2.2, page 85 ... 506 Problem Set 2.3, page 98 ... 509 Problem Set 2.4, page 110 ... 511 Problem Set 2.5, page 122 ... 512 Problem Set 2.6, page 133 ... 513 Problem Set 3.1, page 148 ... 515 Problem Set 3.2, page 157 ... 516 Problem Set 3.3, page 170 ... 517 Problem Set 3.4, page 185 ... 518 Problem Set 3.5, page 196 ... 519 Problem Set 4.3, page 206 ... 520 Problem Set 4.3, page 215 ... 521 Problem Set 4.4, page 225 ... 523 Problem Set 5.1, page 240 ... 524 Problem Set 5.2, page 250 ... 525 Problem Set 5.3, page 262 ... 527 Problem Set 5.4, page 275 ... 528 Problem Set 5.5, page 288 ... 529 Problem Set 5.6, page 302 ... 531 Problem Set 6.1, page 316 ... 532 Problem Set 6.2, page 326 ... 535 Problem Set 6.3, page 327 ... 537 Problem Set 6.4, page 344 ... 538 Problem Set 6.5, page 350 ... 538 Problem Set 7.2, page 357 ... 539 Problem Set 7.3, page 365 ... 540 Problem Set 7.4, page 372 ... 540 Problem Set 8.1, page 381 ... 541 Problem Set 8.2, page 391 ... 542 Problem Set 8.3, page 399 ... 542 Problem Set 8.4, page 406 ... 543 Problem Set 8.5, page 413 ... 543 Problem Set A, page 420 ... 544 Problem Set B, 427 ... 544