# conjugate

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Related to Conjugacy: Beta distribution

## conjugate

1. Maths
a. (of two angles) having a sum of 360°
b. (of two complex numbers) differing only in the sign of the imaginary part as 4 + 3i and 4 -- 3i
c. (of two algebraic numbers) being roots of the same irreducible algebraic equation with rational coefficients
d. (of two elements of a square matrix) interchanged when the rows and columns are interchanged
e. (of two arcs) forming a complete circle or other closed curved figure
2. Chem of, denoting, or concerning the state of equilibrium in which two liquids can exist as two separate phases that are both solutions. The liquid that is the solute in one phase is the solvent in the other
3. Chem (of acids and bases) related by loss or gain of a proton
4. Physics
a. joined by a reciprocal relationship, such as in the case of two quantities, points, etc., that are interchangeable with respect to the properties of each of them
b. (of points connected with a lens) having the property that an object placed at one point will produce an image at the other point
5. (of a compound leaf) having one pair of leaflets

## conjugate

[′kän·jə·gət]
(geology)
Pertaining to fractures in which both sets of veins or joints show the same strike but opposite dip.
Pertaining to any two sets of veins or joints lying perpendicular.
(mathematics)
An element y of a group related to a given element x by y = z -1 xz or zy = xz, where z is another element of the group. Also known as transform.
For a quaternion, x = x0+ x1 i + x2 j + x3 k, the quaternion x̄ = x0-x1 i-x2 j-x3 k.
References in periodicals archive ?
Zalesski, Conjugacy action, induced representations and the Steinberg square for simple groups of Lie type, Proc.
2 Conjugacy classes, Class sums and Character tables
Then G(m) is a union of conjugacy classes for each m.
Section 4 either reviews or derives the needed explicit character values for four kinds of conjugacy classes: the identity element, Singer cycles, semisimple reflections, and transvections.
The admissible class of finite sequences occurring in Theorem 6 is not unique for a given flow, so we can usually choose a convenient A when solving a problem of topological conjugacy.
Robinson, Some special conjugacy closed loops, Canad.
Steinberg, Conjugacy classes, Seminar on Algebraic Groups and Related Finite Groups, Lecture Notes in Math., vol.
Of particular interest is the case n = 1 where both groups are isomorphic G [congruent to] G' = [S.sub.4] but still v interchanges the conjugacy classes [(12)] and [(1234)] (with both 6 elements) and is hence no Hopf algebra isomorphism.
The final two sections cover integrable structures in topological field theories, including the explicit quantum ordering for a special class of quantum geodesic functions, discrete analogues of the Dirac magnetic monopole, and the twistor description of harmonic maps of the Riemann sphere, and algebraic methods in topological field theory and the theory of integrable systems, with discussion of algebras of conjugacy classes of partial elements and Lax operator algebras of type G2.
Avni considers this map on the conjugacy class of fixed-point-free involutions of [S.sub.2n], and the order relation on the permutations in the image of the mapping is the weak Bruhat order.
Here, E([X.sub.K]) denotes the Euler characteristic of [X.sub.K], natural numbers [v.sub.2], [v.sub.2],...,[v.sub.N] denote the orders of primitive elliptic conjugacy classes of [[GAMMA].sub.K] and [[beta].sub.j,k](m) are explicitly given integers.
Conjugacy of morphisms and Lyndon decomposition of standard Sturmian words.

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