# Revision history [back]

This seems to be a bug in maxima, which should be reported. A little googling shows this error has happened before but not with a very clear input matrix. This script in maxima leads straight to a (hopefully debuggable) error:

M: matrix([-d, 0, 0, 0, v, 0, 0, 0, 0, -a], [0, -e, 0, 0, 0, v, 0, 0, 0, a], [0, w, f, 0, 0, 0, v, 0, 0, 0], [0, 0, t, -d, 0, 0, 0, v, 0, 0], [b, 0, 0, 0, -g, 0, 0, 0, 0, 0], [0, b, 0, 0, 0, -g, 0, 0, 0, 0], [0, 0, b, 0, 0, 0, -g, 0, 0, 0], [0, 0, 0, b, 0, 0, 0, -g, 0, 0], [0, 0, -c, 0, 0, 0, 0, 0, -u, 0], [0, 0, c, 0, 0, 0, 0, 0, 0, -u]);
eigenvalues(M);


As a workaround, you can use:

sage: maxima_calculus(M.charpoly()).factor()


which shows you that the characteristic polynomial is of the form linearquadratic^2quintic

sage: M.charpoly().roots()
[(-1/2*Q1 - 1/2*Q4 - 1/2*sqrt(Q1^2 - 2*Q1*Q4 + Q4^2 + 4*A2*omega), 2),
(-1/2*Q1 - 1/2*Q4 + 1/2*sqrt(Q1^2 - 2*Q1*Q4 + Q4^2 + 4*A2*omega), 2),
(-mu_v, 1)]


gives you 3 eigenvalues. The eigenvalue corresponding to the quintic factor is not reported here, likely because maxima (which is used for this if I'm not mistaken) doesn't have access to the means to express that eigenvalue properly.