{"product_id":"linear-algebra-isbn-9781119656920","title":"Linear Algebra","description":"\u003cp\u003e\u003cb\u003ePraise for the \u003ci\u003eThird Edition\u003c\/i\u003e\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e\"This 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 allows the abstract concepts to grow organically out of the necessity to solve specific problems. The intuitive discussions are consistently followed by rigorous statements of results and proofs. \u003ci\u003eLinear Algebra: Ideas and Applications, Fifth Edition\u003c\/i\u003e also features:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eA new application section on section on Google’s Page Rank Algorithm.\u003c\/li\u003e \u003cli\u003eA new application section on pricing long term health insurance at a Continuing Care Retirement Community (CCRC).\u003c\/li\u003e \u003cli\u003eMany other illuminating applications of linear algebra with self-study questions for additional study.\u003c\/li\u003e \u003cli\u003eEnd-of-chapter summaries and sections with true-false questions to aid readers with further comprehension of the presented material\u003c\/li\u003e \u003cli\u003eNumerous computer exercises throughout using MATLAB code\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003e\u003ci\u003eLinear Algebra: Ideas and Applications, Fifth Edition\u003c\/i\u003e is an excellent undergraduate-level textbook for one or two semester undergraduate courses in mathematics, science, computer science, and engineering. With an emphasis on intuition development, the book is also an ideal self-study reference.\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 ℝn 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 ℝn 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 \u003cp\u003e\u003cb\u003eRICHARD C. PENNEY, PHD\u003c\/b\u003e is Emeritus Professor in the Department of Mathematics and former Director of the Mathematics\/Statistics Actuarial Science Program at Purdue University. He has authored numerous journal articles, received several major teaching awards, and is an active researcher. He received his graduate education at MIT.\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePraise for the\u003c\/b\u003e \u003cb\u003e\u003ci\u003eThird Edition\u003c\/i\u003e\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\"This 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.\" —\u003cb\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 allows the abstract concepts to grow organically out of the necessity to solve specific problems. The intuitive discussions are consistently followed by rigorous statements of results and proofs. \u003ci\u003eLinear Algebra: Ideas and Applications, Fifth Edition\u003c\/i\u003e also features:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eA new application section on Google's Page Rank Algorithm.\u003c\/li\u003e \u003cli\u003eA new application section on pricing long term health insurance at a Continuing Care Retirement Community (CCRC).\u003c\/li\u003e \u003cli\u003eMany other illuminating applications of linear algebra with self-study questions for additional study.\u003c\/li\u003e \u003cli\u003eEnd-of-chapter summaries and sections with true-false questions to aid readers with further comprehension of the presented material\u003c\/li\u003e \u003cli\u003eNumerous computer exercises throughout using MATLAB® code\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003e\u003ci\u003eLinear Algebra: Ideas and Applications, Fifth Edition\u003c\/i\u003e is an excellent undergraduate-level textbook for one or two semester undergraduate courses in mathematics, science, computer science, and engineering. With an emphasis on intuition development, the book is also an ideal self-study reference.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989531443429,"sku":"NP9781119656920","price":102.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781119656920.jpg?v=1761784484","url":"https:\/\/k12savings.com\/products\/linear-algebra-isbn-9781119656920","provider":"K12savings","version":"1.0","type":"link"}