frobenius_norm

Frobenius norm. Also known as Schatten 2-norm or Hilbert-Schmidt norm.

\[||\mathbf{A}||_F = \sqrt{\mathrm{trace}(\mathbf{A^*A})}\]

param a:

Complex matrix.

type a:

np.ndarray

returns:

Frobenius norm of the matrix a.

rtype:

float

References

Antoulas, A. Approximation to Large Scale Dynamical Systems. SIAM 2005. Ch 3, Eq 3.5