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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.
Conjugate variables are pairs of thermodynamic concepts, with the first being akin to a "force" applied to some thermodynamic system, the second being akin to the resulting "displacement", and the product of the two equaling the amount of energy transferred. The common conjugate variables are: Pressure-volume (the mechanical parameters);
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 ).
Conjugate (square roots), the change of sign of a square root in an expression; Conjugate element (field theory), a generalization of the preceding conjugations to roots of a polynomial of any degree; Conjugate transpose, the complex conjugate of the transpose of a matrix; Harmonic conjugate in complex analysis
Time and frequency should be probably: the more precisely we now the time a musical note sounded, the less precisely we know its frequency. That phrasing is worse, because when you say "we know the time a musical note sounded", readers will think "time" means "duration", which leads to an incorrect understanding. If you really want to press the analogy with the Heisenberg Uncertainty Principle ...
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 .