{"product_id":"fundamentals-of-matrix-analysis-with-applications-set-isbn-9781118995419","title":"Fundamentals of Matrix Analysis with Applications Set","description":"\u003cp\u003eThis set includes \u003ca title=\"Information about this product: Fundamentals of Matrix Analysis with Applications\" href=\"http:\/\/www.wiley.com\/WileyCDA\/WileyTitle\/productCd-1118953657.html\"\u003eFundamentals of Matrix Analysis with Applications\u003c\/a\u003e \u0026amp; \u003ca title=\"Information about this product: Solutions Manual to Accompany Fundamentals of Matrix Analysis with Applications\" href=\"http:\/\/www.wiley.com\/WileyCDA\/WileyTitle\/productCd-1118996321.html\"\u003eSolutions Manual to Accompany Fundamentals of Matrix Analysis with Applications\u003c\/a\u003e\u003c\/p\u003e \u003cp\u003eProviding comprehensive coverage of matrix theory from a geometric and physical perspective, \u003ci\u003eFundamentals of Matrix Analysis with Applications\u003c\/i\u003e describes the functionality of matrices and their ability to quantify and analyze many practical applications.\u003c\/p\u003e \u003cp\u003eWritten by a highly qualified author team, the book presents tools for matrix analysis and is illustrated with extensive examples and software implementations.\u003c\/p\u003e \u003cp\u003eBeginning with a detailed exposition and review of the Gauss elimination method, the authors maintain readers’ interest with refreshing discussions regarding the issues of operation counts, computer speed and precision, complex arithmetic formulations, parameterization of solutions, and the logical traps that dictate strict adherence to Gauss’s instructions. The book heralds matrix formulation both as notational shorthand and as a quantifier of physical operations such as rotations, projections, reflections, and the Gauss reductions. Inverses and eigenvectors are visualized first in an operator context before being addressed computationally. Least squares theory is expounded in all its manifestations including optimization, orthogonality, computational accuracy, and even function theory. \u003ci\u003eFundamentals of Matrix Analysis with Applications \u003c\/i\u003ealso features:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eNovel approaches employed to explicate the QR, singular value, Schur, and Jordan decompositions and their applications\u003c\/li\u003e \u003cli\u003eCoverage of the role of the matrix exponential in the solution of linear systems of differential equations with constant coefficients\u003c\/li\u003e \u003cli\u003eChapter-by-chapter summaries, review problems, technical writing exercises, select solutions, and group projects to aid comprehension of the presented concepts\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003ePreface\u003c\/p\u003e \u003cp\u003ePart I\u003c\/p\u003e \u003cp\u003eIntroduction: Three Examples\u003c\/p\u003e \u003cp\u003eChapter 1. SYSTEMS OF LINEAR ALGEBRAIC EQUATIONS\u003c\/p\u003e \u003cp\u003e1.1 Linear Algebraic Equations\u003c\/p\u003e \u003cp\u003e1.2 Matrix Representation of Linear Systems and the Gauss]Jordan Algorithm\u003c\/p\u003e \u003cp\u003e1.3 The Complete Gauss Elimination Algorithm\u003c\/p\u003e \u003cp\u003e1.4 Echelon Form and Rank\u003c\/p\u003e \u003cp\u003e1.5 Computational Considerations\u003c\/p\u003e \u003cp\u003eChapter 2. MATRIX ALGEBRA\u003c\/p\u003e \u003cp\u003e2.1 Matrix Multiplication\u003c\/p\u003e \u003cp\u003e2.2 Some Applications of Matrix Operators\u003c\/p\u003e \u003cp\u003e2.3 The Inverse and the Transpose\u003c\/p\u003e \u003cp\u003e2.4 Determinants\u003c\/p\u003e \u003cp\u003e2.5 Three Important Determinant Rules\u003c\/p\u003e \u003cp\u003eReview Problems for Part I\u003c\/p\u003e \u003cp\u003eTechnical Writing Exercises for Part I\u003c\/p\u003e \u003cp\u003eGroup Projects for Part I\u003c\/p\u003e \u003cp\u003eA. LU Factorization\u003c\/p\u003e \u003cp\u003eB. Two]Point Boundary Value Problems\u003c\/p\u003e \u003cp\u003eC. Electrostatic Voltage\u003c\/p\u003e \u003cp\u003eD. Kirchhoff's Laws\u003c\/p\u003e \u003cp\u003eE. Global Positioning Systems\u003c\/p\u003e \u003cp\u003ePart II\u003c\/p\u003e \u003cp\u003eIntroduction: The Structure of General Solutions to Linear Algebraic Equations\u003c\/p\u003e \u003cp\u003eChapter 3. VECTOR SPACES\u003c\/p\u003e \u003cp\u003e3.1 General Spaces, Subspaces, and Spans\u003c\/p\u003e \u003cp\u003e3.2 Linear Dependence\u003c\/p\u003e \u003cp\u003e3.3 Bases, Dimension, and Rank\u003c\/p\u003e \u003cp\u003eChapter 4. ORTHOGONALITY\u003c\/p\u003e \u003cp\u003e4.1 Orthogonal Vectors and the Gram]Schmidt Algorithm Norm\u003c\/p\u003e \u003cp\u003e4.2 Orthogonal Matrices\u003c\/p\u003e \u003cp\u003e4.3 Least Squares\u003c\/p\u003e \u003cp\u003e4.4 Function Spaces\u003c\/p\u003e \u003cp\u003eReview Problems for Part II\u003c\/p\u003e \u003cp\u003eMagic square\u003c\/p\u003e \u003cp\u003eControllability\u003c\/p\u003e \u003cp\u003eTechnical Writing Exercises for Part II\u003c\/p\u003e \u003cp\u003eGroup Projects for Part II\u003c\/p\u003e \u003cp\u003eA. Orthogonal Matrices, Rotations, and Reflections\u003c\/p\u003e \u003cp\u003eB. Householder Reflectors and the QR Factorization\u003c\/p\u003e \u003cp\u003eC. Infinite Dimensional Matrices\u003c\/p\u003e \u003cp\u003ePart III\u003c\/p\u003e \u003cp\u003eIntroduction: Reflect on This\u003c\/p\u003e \u003cp\u003eChapter 5. Eigenvalues and Eigenvectors\u003c\/p\u003e \u003cp\u003e5.1 Eigenvector Basics\u003c\/p\u003e \u003cp\u003e5.2 Calculating Eigenvalues and Eigenvectors\u003c\/p\u003e \u003cp\u003e5.3 Symmetric and Hermitian Matrices\u003c\/p\u003e \u003cp\u003eChapter 5. Summary\u003c\/p\u003e \u003cp\u003eChapter 6. Similarity\u003c\/p\u003e \u003cp\u003e6.1 Similarity Transformations and Diagonalizability\u003c\/p\u003e \u003cp\u003e6.2 Principal Axes Normal Modes\u003c\/p\u003e \u003cp\u003e6.3 Schur Decomposition and Its Implications\u003c\/p\u003e \u003cp\u003e6.4 The Power Method and the QR Algorithm\u003c\/p\u003e \u003cp\u003eChapter 7. Linear Systems of Differential Equations\u003c\/p\u003e \u003cp\u003e7.1 First Order Linear Systems of Differential Equations\u003c\/p\u003e \u003cp\u003e7.2 The Matrix Exponential Function\u003c\/p\u003e \u003cp\u003e7.3 The Jordan Normal Form\u003c\/p\u003e \u003cp\u003eReview Problems for Part III\u003c\/p\u003e \u003cp\u003eTechnical Writing Exercises for Part III\u003c\/p\u003e \u003cp\u003eGroup Projects for Part III\u003c\/p\u003e \u003cp\u003eA. Positive Definite Matrices\u003c\/p\u003e \u003cp\u003eB. Hessenberg Form\u003c\/p\u003e \u003cp\u003eC. The Discrete Fourier Transform and Circulant Matrices\u003c\/p\u003e \u003cp\u003eAnswers to Odd]Numbered Problems\u003c\/p\u003e \u003cp\u003eIndex\u003c\/p\u003e  \u003cp\u003e\u003cstrong\u003eEdward Barry Saff, PhD,\u003c\/strong\u003e?is Professor of Mathematics and Director of the Center for Constructive Approximation at Vanderbilt University. Dr. Saff is an Inaugural Fellow of the American Mathematical Society, Foreign Member of the Bulgarian Academy of Science, and the recipient of both a Guggenheim and Fulbright Fellowship. He is Editor-in-Chief of two research journals,?\u003cem\u003eConstructive Approximation?and?Computational Methods\u003c\/em\u003e and \u003cem\u003eFunction Theory\u003c\/em\u003e, and has authored or coauthored over 250 journal articles and eight books. Dr. Saff also serves as an organizer for a sequence of international research conferences that help to foster the careers of mathematicians from developing countries. \u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eArthur Da vid Snider, PhD, PE,\u003c\/strong\u003e is Professor Emeritus at the University of South Florida, where he served on the faculties of the Departments of Mathematics, Physics, and Electrical Engineering. Previously an analyst at the Massachusetts Institute of Technology's Draper Lab and recipient of the USF Krivanek Distinguished Teacher Award, he consults in industry and has authored or coauthored over 100 journal articles and eight books. With the support of the National Science Foundation, Dr. Snider also pioneered a course in fine art appreciation for engineers.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989261271269,"sku":"NP9781118995419","price":145.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781118995419.jpg?v=1761783422","url":"https:\/\/k12savings.com\/products\/fundamentals-of-matrix-analysis-with-applications-set-isbn-9781118995419","provider":"K12savings","version":"1.0","type":"link"}