congruence transformation

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 ?
It is clear that the transformation introduced in Theorem 1.1 preserves the structure of the pencil, but note that in the real case or in the complex case with * being the complex conjugate, this transformation is a congruence transformation, while in the complex case with * being the transpose, this is just a structure preserving equivalence transformation but not a congruence transformation.
The Algorithm of Calculating Congruence Transformation Matrix.
Yang, "Stable and efficient reduction of large, multiport RC networks by pole analysis via congruence transformations," IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol.
By performing a congruence transformation to the pencil with [X.sup.T] NX, [X.sup.T] HX in (B.6) with an appropriate permutation, we obtain the structured Kronecker form (2.2) of [alpha]N - [beta]H.
We derive numerical methods to compute the characteristic quantities of the Kronecker canonical form of [alpha]N-[beta]H under structure preserving congruence transformations