How expensive is it to compute the eigenvalues of a matrix?

Question

How expensive is it to compute the eigenvalues of a matrix?

What is the complexity of the best algorithms?

How long might it take in practice if I have a 1

Answer 1

I assume it helps if the matrix is sparse?

Yes, there are algorithms, that perform well on sparse matrices.

See for example: http://www.cise.ufl.edu/research/sparse/