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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.
These forces and their associated displacements are called conjugate variables. [1] For example, consider the p V {\displaystyle pV} conjugate pair. The pressure p {\displaystyle p} acts as a generalized force: Pressure differences force a change in volume d V {\displaystyle \mathrm {d} V} , and their product is the energy lost by the system ...
A conjugate prior is an algebraic convenience, giving a closed-form expression for the posterior; otherwise, numerical integration may be necessary. Further, conjugate priors may give intuition by more transparently showing how a likelihood function updates a prior distribution.
The contemporary conjugate convective heat transfer model was developed after computers came into wide use in order to substitute the empirical relation of proportionality of heat flux to temperature difference with heat transfer coefficient which was the only tool in theoretical heat convection since the times of Newton. This model, based on a ...
Conjugate transpose, the complex conjugate of the transpose of a matrix; Harmonic conjugate in complex analysis; Conjugate (graph theory), an alternative term for a line graph, i.e. a graph representing the edge adjacencies of another graph; In group theory, various notions are called conjugation: Inner automorphism, a type of conjugation ...
In mathematics and mathematical optimization, the convex conjugate of a function is a generalization of the Legendre transformation which applies to non-convex functions. It is also known as Legendre–Fenchel transformation , Fenchel transformation , or Fenchel conjugate (after Adrien-Marie Legendre and Werner Fenchel ).
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Equivalently, is conjugate to in if and only if and satisfy the Cauchy–Riemann equations in . As an immediate consequence of the latter equivalent definition, if is any harmonic function on , the function is conjugate to for then the Cauchy–Riemann equations are just = and the symmetry of the mixed second order derivatives, =.