Geodesic
On the sensitivity of the canonical angles of a unitoid
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 25 (2022) no. 4, pp. 403-408.

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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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Kh. D. Ikramov; A. M. Nazari. On the sensitivity of the canonical angles of a unitoid. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 25 (2022) no. 4, pp. 403-408. http://geodesic.mathdoc.fr/item/SJVM_2022_25_4_a4/

[1] R. A. Horn, C. R. Johnson, Matrix Analysis, Second edition, Cambridge University Press, Cambridge, 2013