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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 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?

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 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?

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 reflection) rotation) 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?

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) 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?