Frobenius Norm

• The Frobenius norm, sometimes also called the Euclidean norm
• [Lp Regularization](Lp Regularization.md)
• When p = q = 2 for the $L_{p,q}norm$, it is called the Frobenius norm or the Hilbert–Schmidt norm, though the latter term is used more frequently in the context of operators on (possibly infinite-dimensional) Hilbert space.

$$\Vert A{\Vert }_{\text{F}}=\sqrt{\sum _i^m\sum _j^n|a_{ij}{|}^2}=\sqrt{\mathrm{trace}\left(A^{\ast }A\right)}=\sqrt{\sum _{i=1}^{\min \{m,n\}}{\sigma }_i^2(A)},$$

• where ${\sigma }_i(A)$ are the singular values of A