{"product_id":"linear-algebra-9781119656920","title":"Linear Algebra","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003ePraise for the \u003ci\u003eThird Edition\u003c\/i\u003e\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eThis volume is ground-breaking in terms of mathematical texts in that it does not teach from a detached perspective, but instead, looks to show students that competent mathematicians bring an intuitive understanding to the subject rather than just a master of applications.\u003cbr\u003e\u003ci\u003eElectric Review\u003c\/i\u003e\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eLearn foundational and advanced topics in linear algebra with this concise and approachable resource\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eA comprehensive introduction, \u003ci\u003eLinear Algebra: Ideas and Applications, Fifth Edition\u003c\/i\u003e provides a discussion of the theory and applications of linear algebra that blends abstract and computational concepts. With a focus on the development of mathematical intuition, the book emphasizes the need to understand both the applications of a particular technique and the mathematical ideas underlying the technique.\u003c\/p\u003e \u003cp\u003eThe book introduces each new concept in the context of explicit numerical examples, which allow\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003ePreface xi\u003c\/p\u003e \u003cp\u003eFeatures of the Text xiii\u003c\/p\u003e \u003cp\u003eAcknowledgments xvii\u003c\/p\u003e \u003cp\u003eAbout the Companion Website xviii\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Systems of Linear Equations 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 The Vector Space of m × n Matrices 1\u003c\/p\u003e \u003cp\u003eThe Space ℝ\u003csup\u003en\u003c\/sup\u003e 4\u003c\/p\u003e \u003cp\u003eLinear Combinations and Linear Dependence 7\u003c\/p\u003e \u003cp\u003eWhat Is a Vector Space? 11\u003c\/p\u003e \u003cp\u003eWhy Prove Anything? 15\u003c\/p\u003e \u003cp\u003eExercises 16\u003c\/p\u003e \u003cp\u003e1.1.1 Computer Projects\/Exercises\/Exercises 22\u003c\/p\u003e \u003cp\u003eExercises 24\u003c\/p\u003e \u003cp\u003e1.1.2 Applications to Graph Theory I 25\u003c\/p\u003e \u003cp\u003eExercises 27\u003c\/p\u003e \u003cp\u003e1.2 Systems 27\u003c\/p\u003e \u003cp\u003eRank: The Maximum Number of Linearly Independent Equations 34\u003c\/p\u003e \u003cp\u003eExercises 37\u003c\/p\u003e \u003cp\u003e1.2.1 Computer Projects\/Exercises 39\u003c\/p\u003e \u003cp\u003eExercises 39\u003c\/p\u003e \u003cp\u003e1.2.2 Applications to Circuit Theory 40\u003c\/p\u003e \u003cp\u003eExercises 44\u003c\/p\u003e \u003cp\u003e1.3 Gaussian Elimination 46\u003c\/p\u003e \u003cp\u003eSpanning in Polynomial Spaces 56\u003c\/p\u003e \u003cp\u003eComputational Issues: Pivoting 59\u003c\/p\u003e \u003cp\u003eExercises 60\u003c\/p\u003e \u003cp\u003e1.3.1 Using tolerances in MATLAB’s rref and rank 66\u003c\/p\u003e \u003cp\u003eUsing Tolerances in rref and Rank 66\u003c\/p\u003e \u003cp\u003eExercises 67\u003c\/p\u003e \u003cp\u003e1.3.2 Applications to Traffic Flow 68\u003c\/p\u003e \u003cp\u003eExercises 70\u003c\/p\u003e \u003cp\u003e1.4 Column Space and Nullspace 71\u003c\/p\u003e \u003cp\u003eSubspaces 74\u003c\/p\u003e \u003cp\u003eExercises 82\u003c\/p\u003e \u003cp\u003e1.4.1 Computer Projects\/Exercises 89\u003c\/p\u003e \u003cp\u003eExercises 90\u003c\/p\u003e \u003cp\u003eChapter Summary 91\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Linear Independence and Dimension 93\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 The Test for Linear Independence 93\u003c\/p\u003e \u003cp\u003eBases for the Column Space 100\u003c\/p\u003e \u003cp\u003eTesting Functions for Independence 102\u003c\/p\u003e \u003cp\u003eExercises 104\u003c\/p\u003e \u003cp\u003e2.1.1 Computer Projects\/Exercises 108\u003c\/p\u003e \u003cp\u003eExercises 108\u003c\/p\u003e \u003cp\u003e2.2 Dimension 109\u003c\/p\u003e \u003cp\u003eExercises 118\u003c\/p\u003e \u003cp\u003e2.2.1 Computer Projects\/Exercises 123\u003c\/p\u003e \u003cp\u003eExercises 123\u003c\/p\u003e \u003cp\u003e2.2.2 Applications to Differential Equations 125\u003c\/p\u003e \u003cp\u003eExercises 128\u003c\/p\u003e \u003cp\u003e2.3 Row Space and the Rank-Nullity Theorem 128\u003c\/p\u003e \u003cp\u003eBases for the Row Space 130\u003c\/p\u003e \u003cp\u003eComputational Issues: Computing Rank 138\u003c\/p\u003e \u003cp\u003eExercises 140\u003c\/p\u003e \u003cp\u003e2.3.1 Computer Projects\/Exercises 143\u003c\/p\u003e \u003cp\u003eExercises 143\u003c\/p\u003e \u003cp\u003eChapter Summary 144\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Linear Transformations 147\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 The Linearity Properties 147\u003c\/p\u003e \u003cp\u003eExercises 155\u003c\/p\u003e \u003cp\u003e3.1.1 Computer Projects\/Exercises 160\u003c\/p\u003e \u003cp\u003eExercises 161\u003c\/p\u003e \u003cp\u003e3.2 Matrix Multiplication (Composition) 162\u003c\/p\u003e \u003cp\u003ePartitioned Matrices 169\u003c\/p\u003e \u003cp\u003eComputational Issues: Parallel Computing 171\u003c\/p\u003e \u003cp\u003eExercises 171\u003c\/p\u003e \u003cp\u003e3.2.1 Computer Projects\/Exercises 177\u003c\/p\u003e \u003cp\u003e3-D Computer Graphics 177\u003c\/p\u003e \u003cp\u003eExercises 177\u003c\/p\u003e \u003cp\u003e3.2.2 Applications to Graph Theory II 178\u003c\/p\u003e \u003cp\u003eExercises 180\u003c\/p\u003e \u003cp\u003e3.2.3 Computer Projects\/Exercises 180\u003c\/p\u003e \u003cp\u003eGoogle’s Page Rank Algorithm 180\u003c\/p\u003e \u003cp\u003eExercises 183\u003c\/p\u003e \u003cp\u003e3.3 Inverses 184\u003c\/p\u003e \u003cp\u003eComputational Issues: Reduction versus Inverses 190\u003c\/p\u003e \u003cp\u003eExercises 192\u003c\/p\u003e \u003cp\u003e3.3.1 Computer Projects\/Exercises 197\u003c\/p\u003e \u003cp\u003eIll-Conditioned Systems 197\u003c\/p\u003e \u003cp\u003eExercises 197\u003c\/p\u003e \u003cp\u003e3.3.2 Applications to Economics: The Leontief Open Model 199\u003c\/p\u003e \u003cp\u003eExercises 204\u003c\/p\u003e \u003cp\u003e3.4 The LU Factorization 205\u003c\/p\u003e \u003cp\u003eExercises 213\u003c\/p\u003e \u003cp\u003e3.4.1 Computer Projects\/Exercises 216\u003c\/p\u003e \u003cp\u003eExercises 216\u003c\/p\u003e \u003cp\u003e3.5 The Matrix of a Linear Transformation 217\u003c\/p\u003e \u003cp\u003eCoordinates 217\u003c\/p\u003e \u003cp\u003eApplication to Differential Equations 225\u003c\/p\u003e \u003cp\u003eIsomorphism 228\u003c\/p\u003e \u003cp\u003eInvertible Linear Transformations 229\u003c\/p\u003e \u003cp\u003eExercises 231\u003c\/p\u003e \u003cp\u003e3.5.1 Computer Projects\/Exercises 236\u003c\/p\u003e \u003cp\u003eGraphing in Skewed-Coordinates 236\u003c\/p\u003e \u003cp\u003eExercises 236\u003c\/p\u003e \u003cp\u003e3.5.2 Computer Projects\/Exercises 237\u003c\/p\u003e \u003cp\u003ePricing Long Term Health Care Insurance 237\u003c\/p\u003e \u003cp\u003eExercises 242\u003c\/p\u003e \u003cp\u003eChapter Summary 242\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Determinants 245\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Definition of the Determinant 245\u003c\/p\u003e \u003cp\u003e4.1.1 The Rest of the Proofs 252\u003c\/p\u003e \u003cp\u003eExercises 256\u003c\/p\u003e \u003cp\u003e4.1.2 Computer Projects\/Exercises 258\u003c\/p\u003e \u003cp\u003e4.2 Reduction and Determinants 259\u003c\/p\u003e \u003cp\u003eExercises 266\u003c\/p\u003e \u003cp\u003e4.2.1 Volume 268\u003c\/p\u003e \u003cp\u003eExercises 271\u003c\/p\u003e \u003cp\u003e4.3 A Formula for Inverses 271\u003c\/p\u003e \u003cp\u003eExercises 275\u003c\/p\u003e \u003cp\u003eChapter Summary 276\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Eigenvectors and Eigenvalues 279\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Eigenvectors 279\u003c\/p\u003e \u003cp\u003eExercises 288\u003c\/p\u003e \u003cp\u003e5.1.1 Computer Projects\/Exercises 291\u003c\/p\u003e \u003cp\u003eExercises 291\u003c\/p\u003e \u003cp\u003e5.1.2 Application to Markov Chains 291\u003c\/p\u003e \u003cp\u003eExercises 294\u003c\/p\u003e \u003cp\u003e5.2 Diagonalization 295\u003c\/p\u003e \u003cp\u003ePowers of Matrices 297\u003c\/p\u003e \u003cp\u003eExercises 299\u003c\/p\u003e \u003cp\u003e5.2.1 Application to Systems of Differential Equations 301\u003c\/p\u003e \u003cp\u003eExercises 304\u003c\/p\u003e \u003cp\u003e5.3 Complex Eigenvectors 304\u003c\/p\u003e \u003cp\u003eComplex Vector Spaces 311\u003c\/p\u003e \u003cp\u003eExercises 312\u003c\/p\u003e \u003cp\u003e5.3.1 Computer Projects\/Exercises 314\u003c\/p\u003e \u003cp\u003eExercises 314\u003c\/p\u003e \u003cp\u003eChapter Summary 314\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Orthogonality 317\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 The Scalar Product in ℝ\u003csup\u003en\u003c\/sup\u003e 317\u003c\/p\u003e \u003cp\u003eOrthogonal\/Orthonormal Bases and Coordinates 321\u003c\/p\u003e \u003cp\u003eExercises 326\u003c\/p\u003e \u003cp\u003e6.2 Projections: The Gram–Schmidt Process 328\u003c\/p\u003e \u003cp\u003eThe QR Decomposition 334\u003c\/p\u003e \u003cp\u003eUniqueness of the QR Factorization 337\u003c\/p\u003e \u003cp\u003eExercises 338\u003c\/p\u003e \u003cp\u003e6.2.1 Computer Projects\/Exercises 341\u003c\/p\u003e \u003cp\u003eExercises 342\u003c\/p\u003e \u003cp\u003e6.3 Fourier Series: Scalar Product Spaces 342\u003c\/p\u003e \u003cp\u003eExercises 350\u003c\/p\u003e \u003cp\u003e6.3.1 Computer Projects\/Exercises 353\u003c\/p\u003e \u003cp\u003eExercises 354\u003c\/p\u003e \u003cp\u003e6.4 Orthogonal Matrices 355\u003c\/p\u003e \u003cp\u003eHouseholder Matrices 360\u003c\/p\u003e \u003cp\u003eExercises 364\u003c\/p\u003e \u003cp\u003e6.4.1 Computer Projects\/Exercises 369\u003c\/p\u003e \u003cp\u003eExercises 369\u003c\/p\u003e \u003cp\u003e6.5 Least Squares 370\u003c\/p\u003e \u003cp\u003eExercises 377\u003c\/p\u003e \u003cp\u003e6.5.1 Computer Projects\/Exercises 380\u003c\/p\u003e \u003cp\u003eExercises 380\u003c\/p\u003e \u003cp\u003e6.6 Quadratic Forms: Orthogonal Diagonalization 381\u003c\/p\u003e \u003cp\u003eThe Spectral Theorem 384\u003c\/p\u003e \u003cp\u003eThe Principal Axis Theorem 385\u003c\/p\u003e \u003cp\u003eExercises 392\u003c\/p\u003e \u003cp\u003e6.6.1 Computer Projects\/Exercises 394\u003c\/p\u003e \u003cp\u003eExercises 395\u003c\/p\u003e \u003cp\u003e6.7 The Singular Value Decomposition (SVD) 396\u003c\/p\u003e \u003cp\u003eApplication of the SVD to Least-Squares Problems 402\u003c\/p\u003e \u003cp\u003eExercises 404\u003c\/p\u003e \u003cp\u003eComputing the SVD Using Householder Matrices 406\u003c\/p\u003e \u003cp\u003eDiagonalizing Matrices Using Householder Matrices 408\u003c\/p\u003e \u003cp\u003e6.8 Hermitian Symmetric and Unitary Matrices 409\u003c\/p\u003e \u003cp\u003eExercises 416\u003c\/p\u003e \u003cp\u003eChapter Summary 418\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Generalized Eigenvectors 421\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Generalized Eigenvectors 421\u003c\/p\u003e \u003cp\u003eExercises 429\u003c\/p\u003e \u003cp\u003e7.2 Chain Bases 431\u003c\/p\u003e \u003cp\u003eJordan Form 438\u003c\/p\u003e \u003cp\u003eExercises 443\u003c\/p\u003e \u003cp\u003eThe Cayley–Hamilton Theorem 444\u003c\/p\u003e \u003cp\u003eChapter Summary 445\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Numerical Techniques 447\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Condition Number 447\u003c\/p\u003e \u003cp\u003eCondition Number 449\u003c\/p\u003e \u003cp\u003eLeast Squares 452\u003c\/p\u003e \u003cp\u003eExercises 453\u003c\/p\u003e \u003cp\u003e8.2 Computing Eigenvalues 454\u003c\/p\u003e \u003cp\u003eIteration 454\u003c\/p\u003e \u003cp\u003eThe QR Method 458\u003c\/p\u003e \u003cp\u003eExercises 464\u003c\/p\u003e \u003cp\u003eChapter Summary 465\u003c\/p\u003e \u003cp\u003eAnswers and Hints 467\u003c\/p\u003e \u003cp\u003eIndex 491\u003c\/p\u003e","brand":"John Wiley 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