In this paper, we show that $Vert xi Vert_r = Vert sum_{i in I}x_i x^*_i Vert^{frac{1}{2}}, Vert xi Vert_c = Vert sum_{i in I}x^*_ix_i Vert^{frac{1}{2}}$ for $xi = sum_{i in I}x_i e_i$ in $M_n(H)$, that subspaces as Hilbert spaces are subspaces as column and row Hilbert spaces, and that the standard dual of column (resp., row) Hilbert spaces is the row (resp., column) Hilbert spaces differently from [1,6]. We define operator Hilbert spaces differently from [10], show that our definition of operator Hilbert spaces is the same as that in [10], show that subspaces as Hilbert spaces are subspaces as operator Hilbert spaces, and for a Hilbert space H we give a matrix norm which is not an operator space norm on H.