On the Sensitivity of the Canonical Angles of a Unitoid Matrix

On the Sensitivity of the Canonical Angles of a Unitoid Matrix

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   are (up to the factor 1/2) the arguments of the eigenvalues of the cosquare of  , which is the matrix  . We derive an esti...

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Veröffentlicht in:Numerical analysis and applications 2022-12, Vol.15 (4), p.331-335
Hauptverfasser: Ikramov, Kh. D., Nazari, A. M.
Format: Artikel
Sprache:eng
Schlagworte:
Eigenvalues
Mathematics
Mathematics and Statistics
Numerical Analysis
Perturbation
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Zusammenfassung: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   are (up to the factor 1/2) the arguments of the eigenvalues of the cosquare of  , which is the matrix  . We derive an estimate for the derivative of an eigenvalue of the cosquare in the direction of the perturbation in   caused by a perturbation in  .
ISSN:1995-4239
1995-4247
DOI:10.1134/S199542392204005X