# 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 ?
When H = kG, G a finite group, the definition of conjugacy classes, class sums and representatives reduce to the usual definitions.
As a and b are two elements of order 2 and 3 in S7 with in their specified conjugacy classes and g = a.
is a conjugacy invariant, equal to the coefficient, by which the conjugacy class of [theta] enters in the Plancherel formula for [pi].
Then equation 1 tells us that the size of the conjugacy class of g is [G : 2N1] = [absolute value of G]/[absolute value of 2N1] = 10/2 = 5.
The size of this conjugacy class is given by the index of the centralizer.
4] but still v interchanges the conjugacy classes [(12)] and [(1234)] (with both 6 elements) and is hence no Hopf algebra isomorphism.
Mann, On the graph related to conjugacy classes of groups, Bull.
An extensive table lists 704 reflective lattices grouped according to the conjugacy classes of their Weyl groups.
This is equal to the number of equivalence classes of primitive words of length n under the conjugacy relation x ~ y if x is a cyclic shift of y.
where C(G) is the set of conjugacy classes of G, [X.
Among specific topics are the role of weak convergence in probability theory, ideals in parabolic sub-algebras of simple Lie algebras, the conjugacy of maximal toral sub-algebras of direct limits of loop algebras, quotients in supergeometry, and symmetry and superstring phenomenology.
In our example, the conjugacy property of the Beta distribution with the binomial likelihood function for z = ([z.

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