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Fundamentals of Matrix Analysis with Applications Set

; Arthur David Snider

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Om boka

This set includes

Fakta

Innholdsfortegnelse

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

Om forfatteren

Edward Barry Saff, PhD,?is Professor of Mathematics and Director of the Center for Constructive Approximation at Vanderbilt University. Dr. Saff is an Inaugural Fellow of the American Mathematical Society, Foreign Member of the Bulgarian Academy of Science, and the recipient of both a Guggenheim and Fulbright Fellowship. He is Editor-in-Chief of two research journals,?Constructive Approximation?and?Computational Methods and Function Theory, and has authored or coauthored over 250 journal articles and eight books. Dr. Saff also serves as an organizer for a sequence of international research conferences that help to foster the careers of mathematicians from developing countries.
Arthur Da vid Snider, PhD, PE, is Professor Emeritus at the University of South Florida, where he served on the faculties of the Departments of Mathematics, Physics, and Electrical Engineering. Previously an analyst at the Massachusetts Institute of Technology's Draper Lab and recipient of the USF Krivanek Distinguished Teacher Award, he consults in industry and has authored or coauthored over 100 journal articles and eight books. With the support of the National Science Foundation, Dr. Snider also pioneered a course in fine art appreciation for engineers.