LEADER 04751nam 2200709 450 001 9910460853703321 005 20200520144314.0 010 $a1-118-99632-1 010 $a1-118-95368-1 035 $a(CKB)3710000000460085 035 $a(EBL)1895800 035 $a(SSID)ssj0001530658 035 $a(PQKBManifestationID)12537119 035 $a(PQKBTitleCode)TC0001530658 035 $a(PQKBWorkID)11531322 035 $a(PQKB)10478913 035 $a(PQKBManifestationID)16040957 035 $a(PQKB)20891689 035 $a(MiAaPQ)EBC4530805 035 $a(MiAaPQ)EBC1895800 035 $a(Au-PeEL)EBL1895800 035 $a(CaPaEBR)ebr11088046 035 $a(OCoLC)908554603 035 $a(EXLCZ)993710000000460085 100 $a20150817h20162016 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt 182 $cc 183 $acr 200 10$aFundamentals of matrix analysis with applications /$fEdward Barry Saff, Arthur David Snider 210 1$aHoboken, New Jersey :$cJohn Wiley & Sons, Inc.,$d2016. 210 4$dİ2016 215 $a1 online resource (410 p.) 300 $aDescription based upon print version of record. 311 $a1-118-95365-7 311 $a1-118-99634-8 320 $aIncludes bibliographical references and index. 327 $aTitle Page; Copyright Page; Contents; Preface; PART I INTRODUCTION: THREE EXAMPLES; Chapter 1 Systems of Linear Algebraic Equations; 1.1 Linear Algebraic Equations; 1.2 Matrix Representation of Linear Systems and the Gauss-Jordan Algorithm ; 1.3 The Complete Gauss Elimination Algorithm; 1.4 Echelon Form and Rank; 1.5 Computational Considerations; 1.6 Summary; Chapter 2 Matrix Algebra; 2.1 Matrix Multiplication; 2.2 Some Physical Applications of Matrix Operators; 2.3 The Inverse and the Transpose; 2.4 Determinants; 2.5 Three Important Determinant Rules; 2.6 Summary; Group Projects for Part I 327 $aA. LU Factorization B. Two-Point Boundary Value Problem; C. Electrostatic Voltage; D. Kirchhoff's Laws; E. Global Positioning Systems; F. Fixed-Point Methods; PART II INTRODUCTION: THE STRUCTURE OF GENERAL SOLUTIONS TO LINEAR ALGEBRAIC EQUATIONS; Chapter 3 Vector Spaces; 3.1 General Spaces, Subspaces, and Spans; 3.2 Linear Dependence; 3.3 Bases, Dimension, and Rank; 3.4 Summary; Chapter 4 Orthogonality; 4.1 Orthogonal Vectors and the Gram-Schmidt Algorithm; 4.2 Orthogonal Matrices; 4.3 Least Squares; 4.4 Function Spaces; 4.5 Summary; Group Projects for Part II; A. Rotations and Reflections 327 $aB. Householder Reflectors C. Infinite Dimensional Matrices; PART III INTRODUCTION: REFLECT ON THIS; Chapter 5 Eigenvectors and Eigenvalues; 5.1 Eigenvector Basics; 5.2 Calculating Eigenvalues and Eigenvectors; 5.3 Symmetric and Hermitian Matrices; 5.4 Summary; Chapter 6 Similarity; 6.1 Similarity Transformations and Diagonalizability; 6.2 Principle Axes and Normal Modes; 6.3 Schur Decomposition and Its Implications; 6.4 The Singular Value Decomposition; 6.5 The Power Method and the QR Algorithm; 6.6 Summary; Chapter 7 Linear Systems of Differential Equations; 7.1 First-Order Linear Systems 327 $a7.2 The Matrix Exponential Function 7.3 The Jordan Normal Form; 7.4 Matrix Exponentiation via Generalized Eigenvectors; 7.5 Summary; Group Projects for Part III; A. Positive Definite Matrices; B. Hessenberg Form; C. Discrete Fourier Transform; D. Construction of the SVD; E. Total Least Squares; F. Fibonacci Numbers; Answers to Odd Numbered Exercises; Index; EULA 330 $aThis book provides comprehensive coverage of matrix theory from a geometric and physical perspective, and the authors address the functionality of matrices and their ability to illustrate and aid in many practical applications. Readers are introduced to inverses and eigenvalues through physical examples such as rotations, reflections, and projections, and only then are computational details described and explored. MATLAB is utilized to aid in reader comprehension, and the authors are careful to address the issue of rank fragility so readers are not flummoxed when MATLAB displays conflict with 606 $aMatrices 606 $aAlgebras, Linear 606 $aOrthogonalization methods 606 $aEigenvalues 608 $aElectronic books. 615 0$aMatrices. 615 0$aAlgebras, Linear. 615 0$aOrthogonalization methods. 615 0$aEigenvalues. 676 $a512.9/434 700 $aSaff$b E. B.$f1944-$057326 702 $aSnider$b Arthur David 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910460853703321 996 $aFundamentals of matrix analysis with applications$92219976 997 $aUNINA