On parametrization of the submanifold of matrices with a fixed structure of Jordan blocks

A. A. Bondar'

Ural State Pedagogical University, Ekaterinburg, Russia

Abstract: We construct some new local diffeomorphism that enables us to study submanifolds of matrices. Using the diffeomorphism, we define the parametrization of the submanifold of complex matrices with a fixed structure of the Jordan blocks of distinguished eigenvalues. Comparative characterization is given for various parametrizations.

Keywords: submanifold of matrices, Jordan form, local diffeomorphism, parametrization.

UDC: 517.984.66

Received: 06.11.2014

DOI: 10.17377/smzh.2015.56.604

 English version: Siberian Mathematical Journal, 2015, 56:6, 996–1008

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