I'm about to use \Hn to denote the Hermitian matrices over a general,
specified field. So first let's document that.
% The space of complex Hermitian n-by-n matrices. Does not reduce to
% merely "H" when n=1 since H^{n} does not mean an n-fold cartesian
-% product of H^{1}.
+% product of H^{1}. The field may also be given rather than assumed
+% to be complex; for example \Hn[3]\of{\mathbb{O}} might denote the
+% 3-by-3 Hermitian matrices with octonion entries.
\newcommand*{\Hn}[1][n]{ \mathcal{H}^{#1} }
\ifdefined\newglossaryentry
\newglossaryentry{Hn}{