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EspañolMATRIX CONGRUENCE
In mathematics, two matrices ''A'' and ''B'' with real entries are called 'congruent' if there exists an invertible matrix ''P'' with real entries such that
:''P''T''AP'' = ''B''
where "T" denotes the matrix transpose.
Matrix congruence arises when considering the effect of change of basis on the Gram matrix attached to a bilinear form or quadratic form on a finite-dimensional vector space.
Sylvester's law of inertia states that two congruent symmetric real matrices have the same numbers of positive, negative, and zero eigenvalues. That is, the number of eigenvalues of each sign is an invariant of the associated quadratic form.
★ Similar matrix
:''P''T''AP'' = ''B''
where "T" denotes the matrix transpose.
Matrix congruence arises when considering the effect of change of basis on the Gram matrix attached to a bilinear form or quadratic form on a finite-dimensional vector space.
Sylvester's law of inertia states that two congruent symmetric real matrices have the same numbers of positive, negative, and zero eigenvalues. That is, the number of eigenvalues of each sign is an invariant of the associated quadratic form.
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See also
★ Similar matrix
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