โ Scribed by Gerald Bourgeois
No coin nor oath required. For personal study only.
We deal with square matrices A, B of dimension d = 2 or 3, over the complex field, such that AB / = BA. We introduce the relations G t : exp(tA + B) = exp(tA) exp(B) and G t : exp(tA + B) = exp(tA) exp(B) = exp(B) exp(tA). In dimension 2 we characterize the (A, B) couples satisfying G t for any t โ N. In dimension 2 or 3 we show that if G t is satisfied for any t โ N, then A and B are simultaneously triangularizable. In this manner, we do not need the 2iฯ -congruence-free postulate anymore, which has been supposed by researchers since 1954.
๐ SIMILAR VOLUMES
We prove that commutative power-associative nilalgebras of dimension 6 over a field of characteristic / = 2, 3, 5 are solvable.
In many biophysical and biochemical experiments one observes the decay of some ligand population by an appropriate system of traps. We analyse this decay for a one-dimensional system of randomly distributed traps, and show that one can distinguish three different regimes. The decay starts with a fr