Congruence of rational matrices defined by an integer matrix

Marcin Gąsiorek

Applied Mathematics and Computation, 2023, vol. 440, issue C

Abstract: We study algorithms that construct an invertible matrix B∈Mn(Z) that defines congruence Btr·X·B=Y of given square rational matrices X,Y∈Mn(Q). We describe a general algorithm and discuss special cases of positive-definite and singular matrices. In the first case, the algorithm solves the decision problem and unequivocally determines if such an integer matrix exists.

Keywords: Matrix congruence; Graph isomorphism; Graph automorphism; Coxeter spectral graph theory; Coxeter matrix; Positive-definite matrices (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:440:y:2023:i:c:s0096300322007111

DOI: 10.1016/j.amc.2022.127639

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