ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Mon, 29 Jan 2024 19:11:05 +0100How to take inverse of matrix with complex entrieshttps://ask.sagemath.org/question/75698/how-to-take-inverse-of-matrix-with-complex-entries/I am trying to find the similarity matrix between two 18 by 18 matrices `K_1` and `K_2` which are cospectral. The `is_similar()` function takes too long to run. We can compute the similarity matrix by finding the transition matrices `S` and Q which diagonalize both `K_1` and `K_2`. In other words, `S^(-1)*K_1*S = H = Q^(-1)*K_2*Q`, where `H` is a diagonal matrix. We then know that `Q*S^(-1)*K_1*S*Q^(-1) = K_2`. My problem now though is that we can't compute `Q^(-1)` or `S^(-1)` since both `Q` and `S` have nasty complex numbers and the inverse method in Sage doesn't run fast enough. Any thoughts on how to quickly compute these inverses?
fyi, I did try using the left and right eigenmatrices to find the similarity matrix, but the eigenvectors didn't line up.luke_mattgreenMon, 29 Jan 2024 19:11:05 +0100https://ask.sagemath.org/question/75698/