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Brief communications

Generalized Jordan normal forms of a finite-dimensional linear operator

S. H. Dalalyan

Chair of Algebra and Geometry, Erevan State University, Erevan, Republic of Armenia

Abstract: We define the Mal'tsev representation of a linear operator on a finite-dimensional linear space and establish the necessary and sufficient conditions for its existence. We obtain a second step generalization of theorems on generalized Jordan normal forms of the first and second kinds.

Keywords: generalized Jordan normal form, finite-dimensional linear operator, characteristic polynomial, companion matrix, second step generalization.

UDC: 512.558+512.643

Presented by the member of Editorial Board: A. M. Bikchentaev
Received: 16.11.2010

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2011, 55:5, 67–69

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