## Elements of Matrix Modeling and Computing with MATLABAs 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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algebraic equations algebraic system application augmented matrix by-hand calculations Chapter coefﬁcients column vectors complex numbers components compute cos(t cosine identity Cramer’s rule cross product deblurring deﬁned Deﬁnition derivative det(A det(D determinant diagonal differential equation discrete Fourier transform dot product eigenvalues eigenvectors elementary matrices end end equal erential equation Exercises ﬁnd Find the homogeneous Find the solution ﬁrst force vector Fourier matrix Fourier transform frequency Gauss elimination given graph heat conduction homogeneous solution illustrated image matrix initial value problem inverse matrix least squares function linear combination MATLAB code MATLAB command method minimum distance NCSU node non-zero normal equations nullspace particular solution plane Pollen Image position vector properties q matrix quadratic real number right side row echelon form row operations row vector Section sin(t sine and cosine solution in R4 solve Subsection temperature Theorem upper triangular variation of parameters vector equation velocity zero