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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2012, Number 2, Pages 23–33 (Mi ivm8430)  
This article is cited in 12 scientific papers (total in 12 papers)

The canonical structure of a pencil of degenerate matrix functions

S. V. Gaidomak

Institute for System Dynamics and Control Theory of Siberian Branch of Russian Academy of Sciences, Irkutsk, Russia
Full-text PDF (212 kB) Citations (12)
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Abstract: In this paper we study global properties of pencil of identically degenerate matrix functions with a compact domain of definition. Matrix functions are assumed to have a constant rank and all roots of the characteristic equation of matrix pencil are assumed to have a constant multiplicity at each point in the domain of definition. We obtain sufficient conditions for the smooth orthogonal similarity of matrix functions to the upper triangular form and sufficient conditions for the smooth equivalence of the pencil of matrix functions to its canonical form. We illustrate the obtained results with simple examples.
Keywords: matrix function, pencil, canonical structure, $p$-smoothly similar matrix functions, $p$-smoothly equivalent matrix pencils.
Received: 10.02.2011
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2012, Volume 56, Issue 2, Pages 19–28
DOI: https://doi.org/10.3103/S1066369X1202003X
Bibliographic databases:
Document Type: Article
UDC: 512.643
Language: Russian
Citation: S. V. Gaidomak, “The canonical structure of a pencil of degenerate matrix functions”, Izv. Vyssh. Uchebn. Zaved. Mat., 2012, no. 2, 23–33; Russian Math. (Iz. VUZ), 56:2 (2012), 19–28
Citation in format AMSBIB
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\paper The canonical structure of a~pencil of degenerate matrix functions
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
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\issue 2
\pages 23--33
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\transl
\jour Russian Math. (Iz. VUZ)
\yr 2012
\vol 56
\issue 2
\pages 19--28
\crossref{https://doi.org/10.3103/S1066369X1202003X}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84862669159}
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    • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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    References:81
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