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.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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.
Structure preserving deflation of infinite eigenvalues in structured pencils
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.
Mathematical modeling of transient responses in a large scale multiconductor system
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
A structured staircase algorithm for skew-symmetric/symmetric pencils
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