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Conjugate variables are pairs of variables mathematically defined in such a way that they become Fourier transform duals, [1] [2] or more generally are related through Pontryagin duality. The duality relations lead naturally to an uncertainty relation—in physics called the Heisenberg uncertainty principle —between them.
Two elements , are conjugate if there exists an element such that =, in which case is called a conjugate of and is called a conjugate of . In the case of the general linear group GL ( n ) {\displaystyle \operatorname {GL} (n)} of invertible matrices , the conjugacy relation is called matrix similarity .
The thermodynamic square can be used as a tool to recall and derive some of the thermodynamic potentials based on conjugate variables. In the above description, the product of two conjugate variables yields an energy. In other words, the conjugate pairs are conjugate with respect to energy.
In linguistics, conjugation (/ ˌ k ɒ n dʒ ʊ ˈ ɡ eɪ ʃ ən / [1] [2]) is the creation of derived forms of a verb from its principal parts by inflection (alteration of form according to rules of grammar). For instance, the verb break can be conjugated to form the words break, breaks, and broke.
In mathematics, two functions are said to be topologically conjugate if there exists a homeomorphism that will conjugate the one into the other. Topological conjugacy, and related-but-distinct § Topological equivalence of flows, are important in the study of iterated functions and more generally dynamical systems, since, if the dynamics of one iterative function can be determined, then that ...
Conjugate closure, the image of a subgroup under the conjugation homomorphisms; Conjugate words in combinatorics; this operation on strings resembles conjugation in groups; Isogonal conjugate, in geometry; Conjugate gradient method, an algorithm for the numerical solution of particular systems of linear equations; Conjugate points, in ...
This is a list of equations, by Wikipedia page under appropriate bands of their field. ... Constitutive equation; Laws of science; Defining equation (physical chemistry)
A detailed review [9] of more than 100 examples of conjugate modeling selected from a list of 200 early and modern publications shows that conjugate methods is now used extensively in a wide range of applications. That also is confirmed by numerous results published after this book appearance (2009) that one may see, for example, at the Web of ...