On the sensitivity of the canonical angles of a unitoid matrix
Saidkhakim Ikramov1, Ali Mohammad Nazari2
1Lomonosov Moscow State University, Moscow, Russia
2University of Arak, Arak, Islamic Republic Iran
Keywords: congruence transformation, unitoid, cosquare, canonical angle, circulant
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.
|
