Geodesic
On the sensitivity of the canonical angles of a unitoid
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 25 (2022) no. 4, pp. 403-408 
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/
@article{SJVM_2022_25_4_a4,
     author = {Kh. D. Ikramov and A. M. Nazari},
     title = {On the sensitivity of the canonical angles of a unitoid},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {403--408},
     year = {2022},
     volume = {25},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2022_25_4_a4/}
}
TY  - JOUR
AU  - Kh. D. Ikramov
AU  - A. M. Nazari
TI  - On the sensitivity of the canonical angles of a unitoid
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 2022
SP  - 403
EP  - 408
VL  - 25
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/SJVM_2022_25_4_a4/
LA  - ru
ID  - SJVM_2022_25_4_a4
ER  - 
%0 Journal Article
%A Kh. D. Ikramov
%A A. M. Nazari
%T On the sensitivity of the canonical angles of a unitoid
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2022
%P 403-408
%V 25
%N 4
%U http://geodesic.mathdoc.fr/item/SJVM_2022_25_4_a4/
%G ru
%F SJVM_2022_25_4_a4

Voir la notice de l'article provenant de la source Math-Net.Ru

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 $A$.

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