superscript when that superscript would be one: $\Nn[1]$,
$\Zn[1]$, $\Qn[1]$, $\Rn[1]$, $\Cn[1]$. However, if the
superscript is (say) two, then it appears: $\Nn[2]$, $\Zn[2]$,
- $\Qn[2]$, $\Rn[2]$, $\Cn[2]$. Likewise we have the $n$-by-$n$
- real-symmetric and complex-Hermitian matrices $\Sn$ and $\Hn$
- respectively; however $\Sn[1]$ and $\Hn[1]$ do not automatically
- simplify because the ``$n$'' does not indicate the arity of a
- Cartesian product in this case.
+ $\Qn[2]$, $\Rn[2]$, $\Cn[2]$.
We also have a few basic set operations, for example the union of
two or three sets: $\union{A}{B}$, $\unionthree{A}{B}{C}$. And of
$\transpose{L}$. Its trace is $\trace{L}$. Another matrix-specific
concept is the Moore-Penrose pseudoinverse of $L$, denoted by
$\pseudoinverse{L}$. Finally, the rank of a matrix $L$ is
- $\rank{L}$.
+ $\rank{L}$. As far as matrix spaces go, we have the $n$-by-$n$
+ real-symmetric and complex-Hermitian matrices $\Sn$ and $\Hn$
+ respectively; however $\Sn[1]$ and $\Hn[1]$ do not automatically
+ simplify because the ``$n$'' does not indicate the arity of a
+ Cartesian product in this case.
The span of a set $X$ is $\spanof{X}$, and its codimension is
$\codim{X}$. The projection of $X$ onto $V$ is $\proj{V}{X}$. The
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