In Hamiltonian mechanics, the linear canonical transformation (LCT) is a family of integral transforms that generalizes many classical transforms. It...

In Hamiltonian mechanics, a canonical transformation is a change of canonical coordinates (q, p) → (Q, P) that preserves the form of Hamilton's equations...

is tightened in the linear canonical transformation, discussed below. From the point of view of the linear canonical transformation, Fresnel diffraction...

published, based upon a stationary phase approximation. Linear canonical transformations are the linear transforms of the time–frequency representation that...

other operations, and can also be further generalized into the linear canonical transformation (LCT). An early definition of the FRFT was introduced by Condon...

from mirrors, etc. A ray transfer matrix can be regarded as a linear canonical transformation. According to the eigenvalues of the optical system, the system...

In mathematics, a linear fractional transformation is, roughly speaking, an invertible transformation of the form z ↦ a z + b c z + d . {\displaystyle...

In linear algebra, a Householder transformation (also known as a Householder reflection or elementary reflector) is a linear transformation that describes...

can be further generalized to linear canonical transformations, which can be visualized as the action of the special linear group SL2(R) on the time–frequency...

communication Limit comparison test, for series convergence Linear canonical transformation, an integral transform Link/cut tree, a data structure for...

homogeneous system. The Bogoliubov transformation is an isomorphism of either the canonical commutation relation algebra or canonical anticommutation relation algebra...

matrices represent the same linear map under two possibly different bases, with P being the change-of-basis matrix. A transformation A ↦ P−1AP is called a similarity...

generalized linear model (GLM) is a flexible generalization of ordinary linear regression. The GLM generalizes linear regression by allowing the linear model...

theorem and canonical commutation relations for details. As Hamiltonian mechanics are generalized by symplectic geometry and canonical transformations are generalized...

homographies, linear fractional transformations, bilinear transformations, and spin transformations (in relativity theory). Möbius transformations are defined...

covariants under the action of the group formed by multidimensional Linear Canonical Transformations. The quantum phase space (QPS) is defined as the set { ⟨ z...

automorphisms of V {\displaystyle V} , i.e. the set of all bijective linear transformations V → V {\displaystyle V\to V} , together with functional composition...

may be called a linear complex structure. A complex structure on a real vector space V {\displaystyle V} is a real linear transformation J : V → V {\displaystyle...

Time-frequency analysis – for processing non-stationary signals Linear canonical transformation Spectral estimation – for determining the spectral content...

for the trace of a linear map. Such a definition can be given using the canonical isomorphism between the space End(V) of linear maps on V and V ⊗ V*...

the canonical heat equation by using the transformation: w ( u ) = e − b u / a {\displaystyle w(u)=e^{-bu/a}} This is the Cole-Hopf transformation. With...

Fourier Transform, the Laplace transform, and linear canonical transformations. These transformations are used in signal processing, optics, and quantum...

such as {x, p} = 1. All transformations of variables which preserve these brackets are allowed as canonical transformations in classical mechanics. Motion...

transformation Least squares, linear least squares Gram–Schmidt process Woodbury matrix identity Vector space Linear combination Linear span Linear independence...

vector space, then there is a canonical map from V to the second dual space of V, that sends a vector v to the linear functional fv defined by fv(λ)...

In mathematics and computer science, a canonical, normal, or standard form of a mathematical object is a standard way of presenting that object as a mathematical...

vector spaces V and W over a field F, a linear map (also called, in some contexts, linear transformation or linear mapping) is a map T : V → W {\displaystyle...

A whitening transformation or sphering transformation is a linear transformation that transforms a vector of random variables with a known covariance matrix...

transformation itself, then the index is called covariant and is denoted with a lower index (subscript). As a simple example, the matrix of a linear operator...

of N {\displaystyle N} . More generally, a nilpotent transformation is a linear transformation L {\displaystyle L} of a vector space such that L k =...