Abstract
A known criterion of the congruence between nonsingular matrices (\(A\) and \(B\) are congruent if and only if their cosquares \(A^{-T}A\) and \(B^{-T}B\) are similar) is interpreted from the group-theoretic viewpoint. This interpretation makes it possible to understand why it is the cosquares of \(A\) and \(B\) that participate in the above criterion.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
R. A. Horn and C. R. Johnson, Matrix Analysis, 2nd ed. (Cambridge University Press, Cambridge, 2013).
C. I. Byrnes and M. A. Gauger, ‘‘Decidability criteria for the similarity problem, with applications to the moduli of linear dynamical systems,’’ Adv. Math. 25 (1), 59–90 (1977).
M. A. Gauger and C. I. Byrnes, ‘‘Characteristics free, improved decidability criteria for the similarity problem,’’ Linear Multilinear Algebra 5 (3), 153–158 (1977).
F. R. Gantmacher, The Theory of Matrices (Nauka, Moscow, 1966; Am. Math. Soc., Providence, RI, 1998).
Author information
Authors and Affiliations
Corresponding author
About this article
Cite this article
Ikramov, K.D. A Criterion of the Congruence of Nonsingular Matrices from the Group-Theoretic Viewpoint. MoscowUniv.Comput.Math.Cybern. 45, 12–15 (2021). https://doi.org/10.3103/S0278641921010027
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S0278641921010027