Email this article A Rational Criterion for Congruence of Square Matrices
- Authors: Ikramov K.D.1
-
Affiliations:
- Moscow Lomonosov State University
- Issue: Vol 240, No 6 (2019)
- Pages: 762-764
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/242830
- DOI: https://doi.org/10.1007/s10958-019-04392-w
- ID: 242830
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Abstract
With a square complex matrix A the matrix pair consisting of its symmetric S(A) = (A + AT)/2 and skew-symmetric K(A) = (A − AT)/2 parts is associated. It is shown that square matrices A and B are congruent if and only if the associated pairs (S(A), K(A)) and (S(B), K(B)) are (strictly) equivalent. This criterion can be verified by a rational calculation, provided that the entries of A and B are rational or rational Gaussian numbers.
About the authors
Kh. D. Ikramov
Moscow Lomonosov State University
Author for correspondence.
Email: ikramov@cs.msu.su
Russian Federation, Moscow
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