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The matrix method is a structural analysis method used as a fundamental principle in many applications in civil engineering. The method is carried out, using either a ...
The transfer-matrix method is a method used in optics and acoustics to analyze the propagation of electromagnetic or acoustic waves through a stratified medium; a stack of thin films. [ 1 ] [ 2 ] This is, for example, relevant for the design of anti-reflective coatings and dielectric mirrors .
It is a matrix method that makes use of the members' stiffness relations for computing member forces and displacements in structures. The direct stiffness method is the most common implementation of the finite element method (FEM). In applying the method, the system must be modeled as a set of simpler, idealized elements interconnected at the ...
The Transition Matrix Method (T-matrix method, TMM) is a computational technique of light scattering by nonspherical particles originally formulated by Peter C. Waterman (1928–2012) in 1965. [ 1 ] [ 2 ] The technique is also known as null field method and extended boundary condition method (EBCM). [ 3 ]
Mueller calculus is a matrix method for manipulating Stokes vectors, which represent the polarization of light. It was developed in 1943 by Hans Mueller. In this technique, the effect of a particular optical element is represented by a Mueller matrix—a 4×4 matrix that is an overlapping generalization of the Jones matrix.
The transfer-matrix method is used when the total system can be broken into a sequence of subsystems that interact only with adjacent subsystems. For example, a three-dimensional cubical lattice of spins in an Ising model can be decomposed into a sequence of two-dimensional planar lattices of spins that interact only adjacently.
In the mathematical discipline of linear algebra, a matrix decomposition or matrix factorization is a factorization of a matrix into a product of matrices. There are many different matrix decompositions; each finds use among a particular class of problems.
For example, when a matrix is sparse, an iterative algorithm can skip many of the steps that a direct approach would necessarily follow, even if they are redundant steps given a highly structured matrix. The core of many iterative methods in numerical linear algebra is the projection of a matrix onto a lower dimensional Krylov subspace, which ...