Frobenius distance

Frobenius distance between the matrix $X_{n}^{\phantom{n}k}$ and $H_n^{\phantom{n}r} W_r^{\phantom{r}k}$,

$$ \lVert X_{n}^{\phantom{n}k} - H_n^{\phantom{n}r} W_r^{\phantom{r}k} \rVert^2 \equiv \sum_{n,k} (X_{n}^{\phantom{n}k} - H_n^{\phantom{n}r} W_r^{\phantom{r}k})^2. $$