{"product_id":"fundamentals-of-matrix-analysis-with-applications-hardback-9781118953655","title":"Fundamentals of Matrix Analysis with Applications (Hardback) 9781118953655","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eFundamentals of Matrix Analysis with Applications\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cfont size=\"4\"\u003eEdward Barry Saff (Author), Arthur David Snider (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781118953655, Wiley\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 20 November 2015\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e408 pages\u003cbr\u003e26.2 x 18.5 x 2.5 cm, 0.844 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e\u003cp\u003e\"Providing comprehensive coverage of matrix theory from a geometric and physical perspective, the book describes the functionality of matrices and their ability to quantify and analyze many practical applications. Written by a highly qualified author team, the book presents tools for matrix analysis and is illustrated with extensive examples and software implementations.\" (Zentralblatt MATH 2016).\u003c\/p\u003e \u003cp\u003e\"This is a straightforward modern introduction to matrices..... a very well done text, probably most suitable for engineering students.\" (Mathematical Association of America 2016).\u003c\/p\u003e\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003e\u003cp\u003e\u003cb\u003eAn accessible and clear introduction to linear algebra with a focus on matrices and engineering applications\u003c\/b\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\u003edescribes the functionality of matrices and their ability to quantify and analyze many practical applications. Written 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\u003e\u003ci\u003eFundamentals of Matrix Analysis with Applications \u003c\/i\u003eis an excellent textbook for undergraduate courses in linear algebra and matrix theory for students majoring in mathematics, engineering, and science. The book is also an accessible go-to reference for readers seeking clarification of the fine points of kinematics, circuit theory, control theory, computational statistics, and numerical algorithms.\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e\u003cp\u003ePreface ix\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart I Introduction: Three Examples 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Systems of Linear Algebraic Equations 5\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Linear Algebraic Equations 5\u003c\/p\u003e \u003cp\u003e1.2 Matrix Representation of Linear Systems and the Gauss-Jordan Algorithm 17\u003c\/p\u003e \u003cp\u003e1.3 The Complete Gauss Elimination Algorithm 27\u003c\/p\u003e \u003cp\u003e1.4 Echelon Form and Rank 38\u003c\/p\u003e \u003cp\u003e1.5 Computational Considerations 46\u003c\/p\u003e \u003cp\u003e1.6 Summary 55\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Matrix Algebra 58\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Matrix Multiplication 58\u003c\/p\u003e \u003cp\u003e2.2 Some Physical Applications of Matrix Operators 69\u003c\/p\u003e \u003cp\u003e2.3 The Inverse and the Transpose 76\u003c\/p\u003e \u003cp\u003e2.4 Determinants 86\u003c\/p\u003e \u003cp\u003e2.5 Three Important Determinant Rules 100\u003c\/p\u003e \u003cp\u003e2.6 Summary 111\u003c\/p\u003e \u003cp\u003eGroup Projects for Part I\u003c\/p\u003e \u003cp\u003eA. LU Factorization 116\u003c\/p\u003e \u003cp\u003eB. Two-Point Boundary Value Problem 118\u003c\/p\u003e \u003cp\u003eC. Electrostatic Voltage 119\u003c\/p\u003e \u003cp\u003eD. Kirchhoff’s Laws 120\u003c\/p\u003e \u003cp\u003eE. Global Positioning Systems 122\u003c\/p\u003e \u003cp\u003eF. Fixed-Point Methods 123\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart II Introduction: The Structure of General Solutions to Linear Algebraic Equations 129\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Vector Spaces 133\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 General Spaces Subspaces and Spans 133\u003c\/p\u003e \u003cp\u003e3.2 Linear Dependence 142\u003c\/p\u003e \u003cp\u003e3.3 Bases, Dimension, and Rank 151\u003c\/p\u003e \u003cp\u003e3.4 Summary 164\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Orthogonality 165\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Orthogonal Vectors and the Gram–Schmidt Algorithm 165\u003c\/p\u003e \u003cp\u003e4.2 Orthogonal Matrices 174\u003c\/p\u003e \u003cp\u003e4.3 Least Squares 180\u003c\/p\u003e \u003cp\u003e4.4 Function Spaces 190\u003c\/p\u003e \u003cp\u003e4.5 Summary 197\u003c\/p\u003e \u003cp\u003eGroup Projects for Part II\u003c\/p\u003e \u003cp\u003eA. Rotations and Reflections 201\u003c\/p\u003e \u003cp\u003eB. Householder Reflectors 201\u003c\/p\u003e \u003cp\u003eC. Infinite Dimensional Matrices 202\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart III Introduction: Reflect on This 205\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Eigenvectors and Eigenvalues 209\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Eigenvector Basics 209\u003c\/p\u003e \u003cp\u003e5.2 Calculating Eigenvalues and Eigenvectors 217\u003c\/p\u003e \u003cp\u003e5.3 Symmetric and Hermitian Matrices 225\u003c\/p\u003e \u003cp\u003e5.4 Summary 232\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Similarity 233\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Similarity Transformations and Diagonalizability 233\u003c\/p\u003e \u003cp\u003e6.2 Principle Axes and Normal Modes 244\u003c\/p\u003e \u003cp\u003e6.3 Schur Decomposition and Its Implications 257\u003c\/p\u003e \u003cp\u003e6.4 The Singular Value Decomposition 264\u003c\/p\u003e \u003cp\u003e6.5 The Power Method and the QR Algorithm 282\u003c\/p\u003e \u003cp\u003e6.6 Summary 290\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Linear Systems of Differential Equations 293\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 First-Order Linear Systems 293\u003c\/p\u003e \u003cp\u003e7.2 The Matrix Exponential Function 306\u003c\/p\u003e \u003cp\u003e7.3 The Jordan Normal Form 316\u003c\/p\u003e \u003cp\u003e7.4 Matrix Exponentiation via Generalized Eigenvectors 333\u003c\/p\u003e \u003cp\u003e7.5 Summary 339\u003c\/p\u003e \u003cp\u003eGroup Projects for Part III\u003c\/p\u003e \u003cp\u003eA. Positive Definite Matrices 342\u003c\/p\u003e \u003cp\u003eB. Hessenberg Form 343\u003c\/p\u003e \u003cp\u003eC. Discrete Fourier Transform 344\u003c\/p\u003e \u003cp\u003eD. Construction of the SVD 346\u003c\/p\u003e \u003cp\u003eE. Total Least Squares 348\u003c\/p\u003e \u003cp\u003eF. Fibonacci Numbers 350\u003c\/p\u003e \u003cp\u003eAnswers to Odd Numbered Exercises 351\u003c\/p\u003e \u003cp\u003eIndex 393\u003c\/p\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematics [\u003ca title=\"See our other books on Mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematics%20%5BPB%5D%22\"\u003ePB\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Wiley","offers":[{"title":"Brand New","offer_id":52421384175896,"sku":"9781118953655","price":98.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9781118953655.jpg?v=1784593945","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/fundamentals-of-matrix-analysis-with-applications-hardback-9781118953655","provider":"Freshly Printed Books","version":"1.0","type":"link"}