Diameter of the commuting graph of ${\mathbb{R}}^{n\times n}$

Abstract

The vertices of commuting graph of ${\mathbb{R}}^{n\times n}$ are non-scalar matrices; the edges are defined as pairs $(u,v)$ satisfying $uv=vu$. For $n⩾3$, the diameter of this graph is at least four; we give a short proof that it is exactly four.

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References in corpus (1)

• On the diameter of the commuting graph of the full matrix ring over the real numbers