Simultaneously diagonalizable matrices and a congruence analog of the commutation condition
Kh.D. Ikramov
Lomonosov Moscow State University, Moscow, Russia
Keywords: unitoid, cosquare, canonical form with respect to congruences, canonical angles, congruence orbit
Abstract
It is well known that if diagonalizable matrices A and B commute, then they can be brought to diagonal form via one and the same similarity transformation. We prove an analog of this statement related to nonsingular unitoid matrices and Hermitian congruence transformations. A matrix is said to be unitoid if it can be brought to diagonal form via a congruence transformation.
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