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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2020, Volume 60, Number 1, Pages 109–115
DOI: https://doi.org/10.31857/S0044466920010147 (Mi zvmmf11019) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Symmetric matrices whose entries are linear functions

A. V. Seliverstov

Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow, 127051 Russia
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DOI: https://doi.org/10.31857/S0044466920010147
Abstract: There exists a large set of real symmetric matrices whose entries are linear functions in several variables such that each matrix in this set is definite at some point, that is, the matrix is definite after substituting some numbers for variables. In particular, this property holds for almost all such matrices of order two with entries depending on two variables. The same property holds for almost all matrices of order two with entries depending on a larger number of variables when this number exceeds the order of the matrix. Some examples are discussed in detail. Some asymmetric matrices are also considered. In particular, for almost every matrix whose entries are linear functions in several variables, the determinant of the matrix is positive at some point and negative at another point.
Key words: linear algebra, symmetric matrix, semidefinite programming, Hessian matrix.
Received: 08.07.2019
Revised: 26.07.2019
Accepted: 18.09.2019
English version:
Computational Mathematics and Mathematical Physics, 2020, Volume 60, Issue 1, Pages 102–108
DOI: https://doi.org/10.1134/S0965542520010121
Bibliographic databases:
Document Type: Article
UDC: 512.643
Language: Russian
Citation: A. V. Seliverstov, “Symmetric matrices whose entries are linear functions”, Zh. Vychisl. Mat. Mat. Fiz., 60:1 (2020), 109–115; Comput. Math. Math. Phys., 60:1 (2020), 102–108
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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