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.
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
Biography
Robert E. White
