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2 % Standard operations from linear algebra.
5 % Needed for \lvert, \rVert, etc. and \operatorname.
10 % Absolute value (modulis) of a scalar.
11 \newcommand*
{\abs}[1]{ \left\lvert {#1} \right\rvert }
14 \newcommand*
{\norm}[1]{ \left\lVert {#1} \right\rVert }
16 % The inner product between its two arguments.
17 \newcommand*
{\ip}[2]{ \langle {#1},
{#2} \rangle }
19 % The tensor product of its two arguments.
20 \newcommand*
{\tp}[2]{ {#1} \otimes {#2} }
22 % The ``span of'' operator. The name \span is already taken.
23 \newcommand*
{\spanof}[1]{ \operatorname{span
} \of{{#1}} }
25 % The ``co-dimension of'' operator.
26 \newcommand*
{\codim}{ \operatorname{codim
} }
28 % The trace of an operator.
29 \newcommand*
{\trace}[1]{ \operatorname{trace
} \of{{#1}} }
31 % The orthogonal projection of its second argument onto the first.
32 \newcommand*
{\proj}[2] { \operatorname{proj
}\of{#1,
#2} }
34 % The ``Automorphism group of'' operator.
35 \newcommand*
{\Aut}[1]{ \operatorname{Aut
} \of{{#1}} }
37 % The ``Lie algebra of'' operator.
38 \newcommand*
{\Lie}[1]{ \operatorname{Lie
} \of{{#1}} }
40 % The ``write a matrix as a big vector'' operator.
41 \newcommand*
{\vectorize}[1]{ \operatorname{vec
} \of{{#1}} }
43 % The ``write a big vector as a matrix'' operator.
44 \newcommand*
{\matricize}[1]{ \operatorname{mat
} \of{{#1}} }
46 % The inverse of the adjoint of an operator (the argument).
47 \newcommand*
{\adjinv}[1]{ \left(
{#1}^
{*
} \right)^
{-
1} }
49 % An inline column vector, with parentheses and a transpose operator.
50 \newcommand*
{\colvec}[1]{ \left(
{#1} \right)^
{T
} }