matrices $A$ and $B$ is $\kp{A}{B}$. The adjoint of the operator
$L$ is $\adjoint{L}$, or if it's a matrix, then its transpose is
$\transpose{L}$. Its trace is $\trace{L}$, and its spectrum---the
- set of its eigenvalues---is $\spectrum{L}$. Another matrix-specific
- concept is the Moore-Penrose pseudoinverse of $L$, denoted by
- $\pseudoinverse{L}$. Finally, the rank of a matrix $L$ is
- $\rank{L}$. As far as matrix spaces go, we have the $n$-by-$n$
+ set of its eigenvalues---is $\spectrum{L}$. Another
+ matrix-specific concept is the Moore-Penrose pseudoinverse of $L$,
+ denoted by $\pseudoinverse{L}$. Finally, the rank of a matrix $L$
+ is $\rank{L}$. 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.
+ Cartesian product in this case. A handy way to represent the
+ matrix $A \in \Rn[n \times n]$ whose only non-zero entries are on
+ the diagonal is $\diag{\colvec{A_{11},A_{22},\ldots,A_{nn}}}$.
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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