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Journal Articles Bulletin of the Australian Mathematical Society Year : 2014

## PROPERTY L AND COMMUTING EXPONENTIALS IN DIMENSION AT MOST THREE

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#### Abstract

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

Mathematics [math] Algebraic Geometry [math.AG]

### Dates and versions

hal-03417858 , version 1 (05-11-2021)

### Identifiers

• HAL Id : hal-03417858 , version 1
• DOI :

### Cite

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⟩

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