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≤3. We show that the following conditions are equivalent (i) There exists a finite subset U⊂N≥2 such that for every t∈N∖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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