Abstract
A unitoid matrix is a square complex matrix that can be brought to diagonal form by a Hermitian congruence transformation. The canonical angles of a nonsingular unitoid matrix \(A\) are (up to the factor 1/2) the arguments of the eigenvalues of the cosquare of \(A\), which is the matrix \(A^{-*}A\). We derive an estimate for the derivative of an eigenvalue of the cosquare in the direction of the perturbation in \(A^{-*}A\) caused by a perturbation in \(A\).
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REFERENCES
Horn, R.A. and Johnson, C.R., Matrix Analysis, 2nd ed., Cambridge: Cambridge University Press, 2013.
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Translated from Sibirskii Zhurnal Vychislitel’noi Matematiki, 2022, Vol. 25, No. 4, pp. 403-408. https://doi.org/10.15372/SJNM20220405.
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Ikramov, K.D., Nazari, A.M. On the Sensitivity of the Canonical Angles of a Unitoid Matrix. Numer. Analys. Appl. 15, 331–335 (2022). https://doi.org/10.1134/S199542392204005X
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DOI: https://doi.org/10.1134/S199542392204005X