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.Fri, 10 Jan 2020 23:05:24 +0100Eigenvalues and eigenspaces of orthogonal (or rotation) matriceshttps://ask.sagemath.org/question/49496/eigenvalues-and-eigenspaces-of-orthogonal-or-rotation-matrices/Given an orthogonal transformation of finite order, e.g.
Matrix([[0,0,0,-1],[1,0,0,-1],[0,1,0,-1],[0,0,1,-1]])
Its eigenvalues are going to be of the form
exp(I*pi/5),exp(2*I*pi/5),...,exp(2*I*pi*m),...
corresponding to a splitting of the matrix into rotation (and reflection) matrices. I'd like to extract these fractions `m` (mod ZZ) and study the corresponding (real rotation and reflection) eigenspaces.
My impression is that Sage isn't suitable for doing this directly, but that I should use e.g. the Maxima or Mathematica interface? Any suggestions for the most suitable method?Bob67846Fri, 10 Jan 2020 23:05:24 +0100https://ask.sagemath.org/question/49496/