# congruence transformation

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## congruence transformation

[kən′grü·əns ‚tranz·fər‚mā·shən]
(mathematics)
Also known as transformation.
A mapping which associates with each real quadratic form on a set of coordinates the quadratic form that results when the coordinates are subjected to a linear transformation.
A mapping which associates with each square matrix A the matrix B = SAT, where S and T are nonsingular matrices, and T is the transpose of S ; if A represents the coefficients of a quadratic form, then this definition is equivalent to definition 1.
References in periodicals archive ?
For [tau] to be a congruence relation on X(I), we must show that for all (x,yI) /= (0, 0) in X(I), (a,bI)[tau] (c, dI) implies that (a,bI) * (x,yI) [tau] (c,dI) * [x,yl) and [x,yI) * (a, bI) [tau] (x,yI) * (c, dI).
D]) [right arrow] D [conjunction] X = D [conjunction] Y, where X, Y in I(M)" is a congruence relation.
2) follows from the following congruence relation of polynomials modulo the ideal ([x.
Let X be a SU-algebra, I be an ideal of X and ~ be a congruence relation on X.
It follows by transitivity of the congruence relation.
First, we define a structural congruence relation P [equivalent] Q, capturing the fact that, for example, the order of the branches in a parallel composition has no effect on its behavior.
Let X be a SU-algebra, I be an ideal of X and = be a congruence relation on X.
In this paper we consider a collection of filters and use congruence relation with respect to filters to define a uniformity and make the BS-algebra into a uniform topological space with the desired subset as the open sets.
Let ~ be a congruence relation on a KU-algebra G and let A be an ideal of G.
In the study of the structure of rpp semigroups, Fountain[1] considered a Green-like right congruence relation L* on a semigroup S defined by (a, b [member of] S)aL*b if and only if ax = ay [?
The second section provides a background for the congruence relations examined in this study and offers a central research hypothesis.
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