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 ?
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
12] by performing another block Gau[beta] congruence transformation with pivot blocks I [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.
By performing a congruence transformation to the pencil with [X.
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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