is described by the transposed of the matrix $M$, and $u_{ji}=a_j-b_i$.

([@ei88], Definition 1.1) A matrix $M=(F_{ij})$ is [*1-generic*]{} if the entries in each row or column are linearly independent over $k$.

\[1gen\] It is shown in [@ei88] that the ideal generated by the maximal minors of a 1-generic matrix defines a reduced and irreducible standard determinantal scheme. Clearly 1-genericity is preserved if we delete a row of the matrix. Therefore, the ideal of maximal minors of a 1-generic matrix defines a reduced and irreducible good determinantal scheme.

In this note we study standard and good determinantal schemes, and schemes whose hyperplane section is standard or good determinantal.

Let $S\subseteq{\mathbb{P}}^{n+1}$ be a projective scheme of dimension $d\geq 1$. Let $H$ be a hyperplane. If $H$ does not contain any component of $S$, we say that $S\cap H\subseteq H={\mathbb{P}}^n$ is a [*proper hyperplane section*]{} of $S$.

Fix a geometric property $\mathcal P$. We say that $\mathcal P$ holds for a [*general hyperplane section*]{} of $S$ if there is a nonempty open set $\mathcal V$ (in the ${\mathbb{P}}^{n+1}$ parameterizing hyperplanes in ${\mathbb{P}}^{n+1}$) such that $S\cap H$ has the property $\mathcal P$ for all $H\in {\mathcal V}$. We call $S\cap
H\subseteq H={\mathbb{P}}^n$ a 