# 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 ?
The conjugacy classes of the dihedral groups are described in the following tables, see [10].
Zalesski, Conjugacy action, induced representations and the Steinberg square for simple groups of Lie type, Proc.
But in [15], the present author introduced Smarandache inverse property loops (IPL), weak inverse property loops (WIPL), G--loops, conjugacy closed loops (CC--loop), central loops, extra loops, A--loops, K--loops, Bruck loops, Kikkawa loops, Burn loops and homogeneous loops.
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.
Avni considers this map on the conjugacy class of fixed-point-free involutions of [S.
The second half of the book develops algorithms for word search and conjugacy search problems, a decision algorithm for the work problem in free solvable groups, and a polynomial time algorithm based on a straight line program.
But in [10], the present author introduced Smarandache : inverse property loops (IPL), weak inverse property loops (WIPL), G-loops, conjugacy closed loops (CC-loop), central loops, extra loops, A-loops, K-loops, Bruck loops, Kikkawa loops, Burn loops and homogeneous loops.
lambda]] be its value on the conjugacy class of type [lambda].
But in this paper, Smarandache : inverse property loops (IPL), weak inverse property loops (WIPL), G-loops, conjugacy closed loops (CC-loop), central loops, extra loops, A-loops, K-loops, Bruck loops, Kikkawa loops, Burn loops and homogeneous loops will be introduced and studied relative to the holomorphs of loops.
theta]] is the irreducible character indexed by [lambda] evaluated on the conjugacy class of cycle type [theta], and [f.
A [normalized] character of a group G is a continuous function which is constant on conjugacy classes, positive definite and evaluates to 1 at the unit element.
Striker and Williams made use of the same argument to obtain the conjugacy of promotion and rowmotion (their name for the Fon-Der-Flaass action) in section 6 of Striker and Williams (2012), so it should be no surprise that our induced actions reduce to promotion in types A and B.

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