Thread: Minimal parameterization of a 7 d.o.f. 3x3 matrix with eigenvalue constraint

Hi there

I would like to minimally parameterize the space of real-valued 3x3 matrices whose 3 eigenvalues have the same magnitude. That should be 3*3-2 = 7 parameters.

Can anybody give me some ideas?

Many thanks.

Hi all

I have realized I have a tighter constraint on the eigenvalues than I previously stated. The eigenvalues of the real 3x3 matrix to be parameterized shoud be s, s*exp(i*theta) and s*exp(-i*theta), where s and theta are both real scalars.

Is such a parameterization possible at all?