TY  - BOOK
AU  - Saff,Edward Barry
TI  - Fundamentals of Matrix Analysis with Applications
T2  - New York Academy of Sciences Series
SN  - 9781118953686
AV  - QA188 .S194 2016 
U1  - 512.9/434 
PY  - 2015///
CY  - Newark
PB  - John Wiley & Sons, Incorporated
KW  - Algebras, Linear
KW  - Eigenvalues
KW  - Matrices
KW  - Orthogonalization methods
KW  - Electronic books
N1  - Intro -- Title 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 -- A. 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 -- B. 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 -- 7.2 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
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ER  -