Gerald Bourgeois

activity

20062014

most citedHow to solve the matrix equation XA-AX=f(X)

2 citations · 3 across the 10 of their papers we have counts for

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Showing 2011Show all

3 papers · 1 filter

math.RA2011

Commmuting exponentials in dimension at most 3

Gerald Bourgeois

Let A,B be two square complex matrices of dimension at most 3. We show that the following conditions are equivalent i) There exists a finite subset U included in {2,3,4,...} such t…

math.RA2011

What about A,B if AB-BA and A commute

Gerald Bourgeois

Let A,B be complex n,n complex matrices such that AB-BA and A commute. We show that, if n=2 then A,B are simultaneously triangularizable and if n>=3 then there exists such a couple…

math.RA2011★ 1 cited

Similar Powers of a Matrix

Gerald Bourgeois

Let $p, q$ be coprime integers such that $∣ p ∣ + ∣ q ∣ > 2$ . We characterize the matrices $A \in M_{n} (C)$ such that $A^{p}$ and $A^{q}$ are similar. If $A$ is invertible, we pr…