[sage-support] Matrix logarithm
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). Is it possible to do in a regular PC ? Best regards! Gustavo -- 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 sage-support+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-support/d6dfeea7-edac-4805-91e0-5a26ecaefa5dn%40googlegroups.com.
Re: [sage-support] Matrix logarithm
On Mon, Apr 18, 2022 at 9:31 AM GUSTAVO TERRA BASTOS 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). > FYI, some options are mentioned in https://math.stackexchange.com/questions/3116315/is-there-a-matrix-logarithm-in-sage > Is it possible to do in a regular PC ? > > Best regards! > Gustavo > > -- > 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 sage-support+unsubscr...@googlegroups.com. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sage-support/d6dfeea7-edac-4805-91e0-5a26ecaefa5dn%40googlegroups.com. -- 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 sage-support+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-support/CAEQuuAWm%2BF45JRR6Hk%2BA_BKno9W%3DbMyK_of8JJBEuFrMUVF%2B-g%40mail.gmail.com.
Re: [sage-support] Matrix logarithm
On Mon, 18 Apr 2022 at 14:30, GUSTAVO TERRA BASTOS 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 sage-support+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-support/CAHVvXxSX2maPwn2Q9De-C7Jheb8NTqeAVAvenkmLxL5e%3DON2Fg%40mail.gmail.com.