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

How long might it take in practice if I have a 1000x1000 matrix?

MATLAB (based on LAPACK) computes on a dual-core 1.83 GHz machine all eigenvalues of a 1000x1000 random in roughly 5 seconds. When the matrix is symmetric, the computation can be done significantly faster and requires only about 1 second.