Property L and commuting exponentials in dimension at most three.

Authors

  • G. Bourgeois University of French Polynesia. Laboratory GAATI

Keywords:

Matrix exponential, Matrix pencil, Property L

Abstract

Let \(A,B\) be two square complex matrices of the same dimension \(n\leq {3}\). We show that the following conditions are equivalent (i) There exists a finite subset \(U\subset\mathbb{N}_{\geq {2}}\) such that for every \(t\in\mathbb{N}\setminus{U}\), \(\exp(tA+B)=\exp(tA)\exp(B)=\exp(B)\exp(tA)\). (ii) The pair \((A,B)\) has property L of Motzkin and Taussky and \(\exp(A+B)=\exp(A)\exp(B)=\exp(B)\exp(A)\). We also characterise the pairs of real matrices \((A,B)\) of dimension three, that satisfy the previous conditions. 10.1017/S0004972713000609

Published

2013-12-02

Issue

Vol. 89 No. 1 (2014)

Section

Articles
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