Prove/ Disprove: Let $n$ be a positive integer. Let $A$, $B$ be two $n \times n$ square matrices over the complex numbers. If $AB = BA$ and $\ker A = \ker A^2$ and $\ker B = \ker B …

Can we characterize all integer matrices that are similar (over $\Bbb Z$) to a full Jordan block with $0$'a on the diagonal? In other words, can we determine the conjugacy class of …

I have a nilpotent lie group $N$ with upper central series $$1 = N_0 \triangleleft N_1 \triangleleft \dots \triangleleft N_k = N$$ which induces the filtration $$0 = \mathfrak{n}_0 …

Fix a flag of subspaces V1 in V2 in V3, etc. all in Cn. Consider the space of pairs of commuting linear transformations A and B such that: A preserves the flag (i.e. A(Vi) is in V …