\mathbb{C}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
}
-% The space of symmetric n-by-n matrices.
+% The space of real symmetric n-by-n matrices.
\providecommand*{\Sn}[1][n]{
\mathcal{S}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
}
+% The space of complex Hermitian n-by-n matrices.
+\providecommand*{\Hn}[1][n]{
+ \mathcal{H}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
+}
+
%
% Basic set operations
%
\providecommand*{\cartprodmany}[3]{ \binopmany{\bigtimes}{#1}{#2}{#3} }
\providecommand*{\directsummany}[3]{ \binopmany{\bigoplus}{#1}{#2}{#3} }
\providecommand*{\unionmany}[3]{ \binopmany{\bigcup}{#1}{#2}{#3} }
+
+
+% The four standard (UNLESS YOU'RE FRENCH) types of intervals along
+% the real line.
+\providecommand*{\intervaloo}[2]{ \left({#1},{#2}\right) } % open-open
+\providecommand*{\intervaloc}[2]{ \left({#1},{#2}\right] } % open-closed
+\providecommand*{\intervalco}[2]{ \left[{#1},{#2}\right) } % closed-open
+\providecommand*{\intervalcc}[2]{ \left[{#1},{#2}\right] } % closed-closed