I am reading this paper where they introduce 4 types of norm penalties which induce sparsity in the matrix block $H_g$ in table 1. For example, $\log/ l_1$ is $\sum_{g} log(\epsilon + \lVert H_{g} \rVert_1)$.
As the definition of $\lVert H_{g} \rVert_1$, it is the maximum absolute column sum of the matrix (wiki). But in the paper, they give a description under the table "all norms are elementwise over matrix entries". How can norm are elementwise? I think from the definition, it seems to be columnwise.