Say we have a matrix P with eigenvalues [itex]\lambda_1, \cdots, \lambda_n[/itex] (possibly some are the same) and P can be diagonalized, then we can always say that the element on the a'th row and b'th column of P^n is equal to [itex]P^n(a,b) = \sum_{i = 1}^n \alpha_i \lambda_i^n [/itex] with [itex]\alpha_i[/itex] independent of n (but dependent on a and b).(adsbygoogle = window.adsbygoogle || []).push({});

Correct? And I don't think the conditions can be weakened?

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# General truth about elements of a matrix to the n-th power?

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