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More About This Textbook
Overview
As discrete models and computing have become more common, there is a need to study matrix computation and numerical linear algebra. Encompassing a diverse mathematical core, Elements of Matrix Modeling and Computing with MATLAB examines a variety of applications and their modeling processes, showing you how to develop matrix models and solve algebraic systems. Emphasizing practical skills, it creates a bridge from problems with two and three variables to more realistic problems that have additional variables.
Elements of Matrix Modeling and Computing with MATLAB focuses on seven basic applications: circuits, trusses, mixing tanks, heat conduction, data modeling, motion of a mass, and image filters. These applications are developed from very simple to more complex models. To explain the processes, the book explores numerous topics in linear algebra, including complex numbers and functions, matrices, algebraic systems, curve fitting, elements of linear differential equations, transform methods, and tools of computation. For example, the author uses linearly independent vectors and subspaces to explain over- and under-determined systems, eigenvalues and eigenvectors to solve initial value problems, and discrete Fourier transforms to perform image filtering in the frequency domain. Although the primary focus is to cultivate calculation skills by hand, most chapters also include MATLAB to help with more complicated calculations.
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Table of Contents
List of Figures List of Tables Preface Introduction
VECTORS IN THE PLANE Floating Point and Complex Numbers Complex Valued Functions Vectors in R2
Dot Product and Work Lines and Curves in R2 and C
VECTORS IN SPACE Vectors and Dot Product Cross and Box Products Lines and Curves in R3
Planes in R3
Extensions to Rn
Ax = d: UNIQUE SOLUTION Matrix Models Matrix Products Special Cases of Ax = d Row Operations and Gauss Elimination Inverse Matrices LU Factorization Determinants and Cramer's Rule
Ax = d: LEAST SQUARES SOLUTION Curve Fitting to Data Normal Equations Multilinear Data Fitting Parameter Identification
Ax = d: MULTIPLE SOLUTIONS Subspaces and Solutions in R3
Row Echelon Form Nullspaces and Equilibrium Equations
LINEAR INITIAL VALUE PROBLEMS First Order Linear Second Order Linear Homogeneous and Complex Solution Nonhomogeneous Linear Differential Equations System Form of Linear Second Order
EIGENVALUES AND DIFFERENTITAL EQUATIONS Solution of x' = Ax by Elimination Real Eigenvalues and Eigenvectors Solution of x' = Ax + f (t)
IMAGE PROCESSING IN THE SPACE DOMAIN Matrices and Images Contrast and Histograms Blurring and Sharpening
IMAGE PROCESSING IN THE FREQUENCY DOMAIN Laplace and Fourier Transforms Properties of DFT DFT in Rn × Rn Frequency Filters in Rn × Rn
Appendix: Solutions to Odd Exercises Bibliography Index