# congruence transformation

(redirected from*Congruence relation*)

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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.McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

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