  It is proved that for any free $\mathcal{A}$-modules $\mathcal{F}$ and
$\mathcal{E}$ of finite rank on some $\mathbb{C}$-algebraized space $(X,
\mathcal{A})$ a \textit{degenerate} bilinear $\mathcal{A}$-morphism $\Phi:
\mathcal{F}\times \mathcal{E}\longrightarrow \mathcal{A}$ induces a
\textit{non-degenerate} bilinear $\mathcal{A}$-morphism $\bar{\Phi}:
\mathcal{F}/\mathcal{E}^\perp\times
\mathcal{E}/\mathcal{F}^\perp\longrightarrow \mathcal{A}$, where
$\mathcal{E}^\perp$ and $\mathcal{F}^\perp$ are the \textit{orthogonal}
sub-$\mathcal{A}$-modules associated with $\mathcal{E}$ and $\mathcal{F}$,
respectively. This result generalizes the finite case of the classical result,
which states that given two vector spaces $W$ and $V$, paired into a field $k$,
the induced vector spaces $W/V^\perp$ and $V/W^\perp$ have the same dimension.
Some related results are discussed as well.
