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 ?
D]) [right arrow] D [conjunction] X = D [conjunction] Y, where X, Y in I(M)" is a congruence relation.
D]) [right arrow] D [disjunction] X = D [disjunction] Y, where X, Y in I(M)" is a congruence relation.
1] [less than or equal to] D" is congruence relation.
Let X be a SU-algebra, I be an ideal of X and ~ be a congruence relation on X.
A congruence relation R on G is a collection of equivalence relations [R.
Suppose that R is a congruence relation on G with the property that the associated quadruple {A, G/R, [sigma]([x]), [alpha]([x], [x])} is a crossed system.
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.
Then consider the uniformity based on congruence relations with respect to given collection of filters and construct the induced topology by this uniformity in [section]3.
If I is an ideal of binary algebra X, then the relation ~ is a congruence relation on X.
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 [?