On Mon, 18 Apr 2022 at 14:30, GUSTAVO TERRA BASTOS <[email protected]> wrote: > > Hi guys. > > Given two n x n matrices M, N, we know it is a big problem to find the > positive integer "i" such that M^i = N (There are other hypothesis involved). > In my particular case, I would like to do the same for 3 x 3 matrices M , N > over F_{11^2} (finite field with 121 elements).
Note that finding this integer i here is something different from what is usually referred to as the "matrix logarithm" (the inverse of the matrix exponential) which gives a matrix rather than an integer as the result. Is it prohibitive to just compute powers of M until you find that M^i = N? Any i would need to satisfy det(M)^i = det(N) which should be faster to solve for large i unless det(M) and det(N) are both zero or one. Otherwise I think you can generalise the approach to other coefficients in the characteristic polynomial. Oscar -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-support/CAHVvXxSX2maPwn2Q9De-C7Jheb8NTqeAVAvenkmLxL5e%3DON2Fg%40mail.gmail.com.
