This article is about the transfer matrix in wavelet theory. For the transfer matrix in control systems, see Transfer function matrix. For the transfer matrix method in statistical physics, see Transfer-matrix method. For the transfer matrix method in optics, see Transfer-matrix method (optics). For the transfer matrix in dynamical systems theory, see Transfer operator. For a single scalar, see Transfer coefficient (disambiguation).
In applied mathematics, the transfer matrix is a formulation in terms of a block-Toeplitz matrix of the two-scale equation, which characterizes refinable functions. Refinable functions play an important role in wavelet theory and finite element theory.
For the mask , which is a vector with component indexes from to ,
the transfer matrix of , we call it here, is defined as
More verbosely
The effect of can be expressed in terms of the downsampling operator "":
In applied mathematics, the transfermatrix is a formulation in terms of a block-Toeplitz matrix of the two-scale equation, which characterizes refinable...
Ray transfermatrix analysis (also known as ABCD matrix analysis) is a mathematical form for performing ray tracing calculations in sufficiently simple...
various branches of engineering, a transfer function matrix, or just transfermatrix is a generalisation of the transfer functions of single-input single-output...
transfer matrix can be obtained for any linear system to analyze its dynamics and other properties; each element of a transfermatrix is a transfer function...
In statistical mechanics, the corner transfermatrix describes the effect of adding a quadrant to a lattice. Introduced by Rodney Baxter in 1968 as an...
parabolic reflector. The ray matrix of a concave spherical mirror is shown here. The C {\displaystyle C} element of the matrix is − 1 f {\displaystyle -{\frac...
The Matrix is a 1999 science fiction action film written and directed by the Wachowskis. It is the first installment in the Matrix film series, starring...
description much later, by Lars Onsager (1944). It is usually solved by a transfer-matrix method, although there exist different approaches, more related to...
− 1 B T P {\displaystyle K=R^{-1}B^{T}P} and the closed loop state transfermatrix is A − B K = A − B R − 1 B T P {\displaystyle A-BK=A-BR^{-1}B^{T}P}...
Schema, a data exchange and access model in biology ABCD matrix analysis, or ray transfermatrix analysis ABCD-parameters, in a two-port network ABCd, an...
function. Bernoulli scheme Shift of finite type Krein–Rutman theorem Transfer-matrix method Gaspard, Pierre (1992). "r-adic one dimensional maps and the...
requires the transfermatrix formalism, though the result is the same. (Click "show" at right to see the details of the transfermatrix formalism.) The...
still exponential in n). Both Conway's and Jensen's versions of the transfer-matrix method involve counting the number of polyominoes that have a certain...
where the 2×2 element τ {\displaystyle \tau } is the beam-splitter transfermatrix and r and t are the reflectance and transmittance along a particular...
combined with the paraxial approximation in techniques such as ray transfermatrix analysis. The focal length, f, of a lens in air is given by the lensmaker's...
three other families come from a transfermatrix T ( λ ) {\displaystyle T(\lambda )} (in turn defined using a Lax matrix), which acts on H {\displaystyle...
approximation is used in Gaussian optics and first-order ray tracing. Ray transfermatrix analysis is one method that uses the approximation. In some cases,...
Dot matrix printing, sometimes called impact matrix printing, is a computer printing process in which ink is applied to a surface using a relatively low-resolution...
{\displaystyle S_{1}} is the transfermatrix between the original beam position and the quadrupole(s), Q {\displaystyle Q} is the transfermatrix of the quadrupole(s)...
by a matrix of organic polymers. PMCs are designed to transfer loads between fibers of a matrix. Some of the advantages with PMCs include their light...
Matrix molding or matrixtransfer molding is a technique often used during molding. The person doing the assembly will first create the rigid outer shell...
matrix is a matrix associated to two univariate polynomials with coefficients in a field or a commutative ring. The entries of the Sylvester matrix of...
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