Solutions manual to accompany fundamentals of matrix analysis with applications
Matrices Algebras, Linear Orthogonalization methods Eigenvalues
Wiley
2016
EISBN 1118996321
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
This 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
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
This 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
