RUS  ENG
Full version
JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. POMI, 2017 Volume 463, Pages 81–93 (Mi znsl6508)

This article is cited in 10 papers

Orthogonality graphs of matrices over skew fields

A. E. Guterman, O. V. Markova

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow, Russia

Abstract: The paper is devoted to studying the orthogonality graph of the matrix ring over a skew field. It is shown that for $n\geq3$ the orthogonality graph of the $n\times n$ matrix ring $M_n(\mathbb D)$ over a skew field $\mathbb D$ is connected and has diameter $4$ for an arbitrary skew field $\mathbb D$. If $n=2$, then the graph of the ring $M_n(\mathbb D)$ is a disjoint union of connected components of diameters $1$ and $2$. As a corollary, we obtain related results on the orthogonality graphs of simple Artinian rings.

Key words and phrases: graphs of matrix relations, orthogonality graph, matrices over a skew field.

UDC: 512.643

Received: 31.10.2017


 English version:
Journal of Mathematical Sciences (New York), 2018, 232:6, 797–804

Bibliographic databases:


© Steklov Math. Inst. of RAS, 2025