siliciooy0j
2022-03-24
mhapo933its
Beginner2022-03-25Added 9 answers
Step 1
This looks like it can get complicated. Generically, at least over an algebraically closed field, a matrix M will have distinct eigenvalues , and generically will have distinct eigenvalues with multiplicity one, and with multiplicity two. Thus the centralizer will have dimension
But there are many degenerate cases: for instance if M has eigenvalues 1 then will have eigenvalues with multiplicities . Things can get more complicated still.
Then M might have non-trivial Jordan blocks, and then the real fun starts!
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