3
votes
Accepted
The rank of a certain linear combination of mutually commuting nilpotent matrices
The result is false, here is a counter exemple :
Let $A_0,A_1,A_2$ as in your exemple. Consider $B_0,B_1,B_2\in\mathcal{M}_4(\mathbb{C})$ defined by block as follow:
$B_i=\begin{pmatrix}0_2&A_i\\...
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