Seminorm

A function p: V → [0,∞) on a vector space V that is positively homogeneous (p(αv)=|α| p(v) for scalars α) and subadditive (p(v+w) ≤ p(v)+p(w)); unlike a norm, p(v)=0 may hold for some nonzero v.

A seminorm p on a vector space is a nonnegative functional satisfying absolute homogeneity p(αv)=|α|p(v) and subadditivity p(u+v)≤p(u)+p(v), but it may vanish on nonzero vectors (its kernel can be nontrivial), so positive definiteness can fail.