Abstract:
This paper presents a light introduction to Perron–Frobenius theory in max algebra and in nonnegative linear algebra, and a survey of results on two cores of a nonnegative matrix. The (usual) core of a
nonnegative matrix is defined as ∩k⩾1span+(Ak), that is, intersection of the nonnegative column spans of matrix powers. This object is of importance in the (usual) Perron-Frobenius theory, and it has some applications in ergodic theory. We develop the direct max-algebraic analogue and follow the similarities and differences of both theories.
The work is partially supported by EPSRC (project no. RRAH15735), S. Sergeev also acknowledges the support of RFBR-CNRS (project no. 11-0193106) and RFBR (project no. 12-01-00886).
Received: 21.06.2019
Document Type:
Article
UDC:512.643
Language: Russian
Citation:
P. Butkovic, H. Schneider, S. Sergeev, “Core of a matrix in max algebra and in nonnegative algebra: a survey”, Russian Universities Reports. Mathematics, 24:127 (2019), 252–271
\Bibitem{ButSchSer19}
\by P.~Butkovic, H.~Schneider, S.~Sergeev
\paper Core of a matrix in max algebra and in nonnegative algebra: a survey
\jour Russian Universities Reports. Mathematics
\yr 2019
\vol 24
\issue 127
\pages 252--271
\mathnet{http://mi.mathnet.ru/vtamu151}
\crossref{https://doi.org/10.20310/2686-9667-2019-24-127-252-271}
Linking options:
https://www.mathnet.ru/eng/vtamu151
https://www.mathnet.ru/eng/vtamu/v24/i127/p252
This publication is cited in the following 1 articles:
Ja-Hee Kim, “An Asymptotic Cyclicity Analysis of Live Autonomous Timed Event Graphs”, Applied Sciences, 11:11 (2021), 4769