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PROPERTY L AND COMMUTING EXPONENTIALS IN DIMENSION AT MOST THREE
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 89 / Issue 1 / February 2014
- Published online by Cambridge University Press:
- 28 June 2013, pp. 70-78
- Print publication:
- February 2014
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- Article
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- You have access
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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.
