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Hi,

if MMM is a square matrix and I-MIMI-M is inversible, we know that

k=0nMk=(I-Mn+1)(I-M)-1superscriptsubscriptk0nsuperscriptMkIsuperscriptMn1superscriptIM1\sum_{{k=0}}^{{n}}M^{k}=(I-M^{{n+1}})(I-M)^{{-1}}

Now I have the following sum :

k=0nMk(MH)ksuperscriptsubscriptk0nsuperscriptMksuperscriptsuperscriptMHk\sum_{{k=0}}^{{n}}M^{k}(M^{H})^{k}

where MMM is a square non hermitian matrix (MHsuperscriptMHM^{H} denotes the hermitian of MMM).

I’d like to know if there exists an explicit formula for this sum, like the previous one.

Thanks,

RB


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