PROPERTY L AND COMMUTING EXPONENTIALS IN DIMENSION AT MOST THREE

Gerald Bourgeois (1)

1 GAATI - Laboratoire de Géométrie Algébrique et Applications à la Théorie de l'Information

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.

Domains: Algebraic Geometry [math.AG]

Gerald Bourgeois. PROPERTY L AND COMMUTING EXPONENTIALS IN DIMENSION AT MOST THREE. Bulletin of the Australian Mathematical Society, 2014, 89 (1), pp.70-78. ⟨10.1017/S0004972713000609⟩. ⟨hal-03417858⟩