# Revision history [back]

### 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?