Frobenius norm
= Frobenius norm
{c}
{title2=$\|A\|_F=(\sum_{i,j}|a_{ij}|^2)^{1/2}$}
The Frobenius norm is the finite-matrix <Hilbert-Schmidt norm>. It equals $\sqrt{\operatorname{tr}(A^*A)}$, is unchanged by unitary multiplication on either side, and is the square root of the sum of squared singular values. For unit vectors $u,v$, $\|uu^*-vv^*\|_F^2=2(1-|u^*v|^2)$, a useful sign-invariant measure of distance between rank-one <orthogonal projection matrices>.