Fundamentals of Matrix Analysis with Applications Set

This set includes Fundamentals of Matrix Analysis with Applications & Solutions Manual to Accompany Fundamentals of Matrix Analysis with Applications Providing comprehensive coverage of matrix theory from a geometric and physical perspective, Fundamentals of Matrix Analysis with Applications 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. Beginning 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. Fundamentals of Matrix Analysis with Applications also features: Novel approaches employed to explicate the QR, singular value, Schur, and Jordan decompositions and their applications Coverage of the role of the matrix exponential in the solution of linear systems of differential equations with constant coefficients Chapter-by-chapter summaries, review problems, technical writing exercises, select solutions, and group projects to aid comprehension of the presented concepts

Table of 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 Chapter 2. MATRIX ALGEBRA 2.1 Matrix Multiplication 2.2 Some Applications of Matrix Operators 2.3 The Inverse and the Transpose 2.4 Determinants 2.5 Three Important Determinant Rules Review Problems for Part I Technical Writing Exercises for Part I Group Projects for Part I A. LU Factorization B. Two]Point Boundary Value Problems C. Electrostatic Voltage D. Kirchhoff's Laws E. Global Positioning Systems 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 Chapter 4. ORTHOGONALITY 4.1 Orthogonal Vectors and the Gram]Schmidt Algorithm Norm 4.2 Orthogonal Matrices 4.3 Least Squares 4.4 Function Spaces Review Problems for Part II Magic square Controllability Technical Writing Exercises for Part II Group Projects for Part II A. Orthogonal Matrices, Rotations, and Reflections B. Householder Reflectors and the QR Factorization C. Infinite Dimensional Matrices Part III Introduction: Reflect on This Chapter 5. Eigenvalues and Eigenvectors 5.1 Eigenvector Basics 5.2 Calculating Eigenvalues and Eigenvectors 5.3 Symmetric and Hermitian Matrices Chapter 5. Summary Chapter 6. Similarity 6.1 Similarity Transformations and Diagonalizability 6.2 Principal Axes Normal Modes 6.3 Schur Decomposition and Its Implications 6.4 The Power Method and the QR Algorithm Chapter 7. Linear Systems of Differential Equations 7.1 First Order Linear Systems of Differential Equations 7.2 The Matrix Exponential Function 7.3 The Jordan Normal Form Review Problems for Part III Technical Writing Exercises for Part III Group Projects for Part III A. Positive Definite Matrices B. Hessenberg Form C. The Discrete Fourier Transform and Circulant Matrices Answers to Odd]Numbered Problems Index