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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2014, Number 12, Pages 70–82 (Mi ivm8959)  
This article is cited in 9 scientific papers (total in 9 papers)

Simultaneous diagonalization of three real symmetric matrices

M. A. Novikov

Institute of System Dynamics and Control Theory, Siberian Branch of the Russian Academy of Sciences, 134 Lermontov str., Irkutsk, 664033 Russia
Full-text PDF (211 kB) Citations (9)
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Abstract: We formulate and prove necessary and sufficient conditions of simultaneous diagonalization of three real symmetric matrices of regular pencil to diagonal ones. The conditions are algebraic and consist, in particular, of two spectral requirements and one matrix equality. For degenerate matrix pencil we suggest an approach that allows to reduce the analysis to a regular pencil. With the use of obtained theorems we investigate a decomposition of linear gyroscopic system into subsystems of an order not higher than two and a stability of trivial solution to a system.
Keywords: matrix pencil, simultaneous diagonalization, real congruent transformation.
Received: 15.05.2013
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2014, Volume 58, Issue 12, Pages 59–69
DOI: https://doi.org/10.3103/S1066369X1412007X
Bibliographic databases:
Document Type: Article
UDC: 512.647
Language: Russian
Citation: M. A. Novikov, “Simultaneous diagonalization of three real symmetric matrices”, Izv. Vyssh. Uchebn. Zaved. Mat., 2014, no. 12, 70–82; Russian Math. (Iz. VUZ), 58:12 (2014), 59–69
Citation in format AMSBIB
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\by M.~A.~Novikov
\paper Simultaneous diagonalization of three real symmetric matrices
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2014
\issue 12
\pages 70--82
\mathnet{http://mi.mathnet.ru/ivm8959}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2014
\vol 58
\issue 12
\pages 59--69
\crossref{https://doi.org/10.3103/S1066369X1412007X}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84924053274}
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    • This publication is cited in the following 9 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:84
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