Howtosignalprocessing
Why do we use Frobenius norm?
The Frobenius norm is useful to measure the RMS (root-mean-square) gain of the matrix, its average response along given mutually orthogonal directions in space. Clearly, this approach does not capture well the variance of the error, only the average effect of noise.
Is Frobenius norm induced?
The Frobenius norm satisfies proposition 1.7 but is not an induced norm, since for In, the identity matrix of order n, we have . For finite dimensional spaces all norms are equivalent. In particular, the Euclidean and Frobenius norms are related to each other by the following inequalities.
