mjo-linear_algebra.tex

   1 %
   2 % Standard operations from linear algebra.
   3 %
   4
   5 % Needed for \operatorname.
   6 \usepackage{amsopn}
   7
   8 \input{mjo-common}
   9
  10 % The inner product between its two arguments.
  11 \newcommand*{\ip}[2]{ \langle {#1}, {#2} \rangle }
  12
  13 % The tensor product of its two arguments.
  14 \newcommand*{\tp}[2]{ {#1} \otimes {#2} }
  15
  16 % The ``span of'' operator. The name \span is already taken.
  17 \newcommand*{\spanof}[1]{ \operatorname{span} \of{{#1}} }
  18
  19 % The ``co-dimension of'' operator.
  20 \newcommand*{\codim}{ \operatorname{codim} }
  21
  22 % The trace of an operator.
  23 \newcommand*{\trace}[1]{ \operatorname{trace} \of{{#1}} }
  24
  25 % The orthogonal projection of its second argument onto the first.
  26 \newcommand*{\proj}[2] { \operatorname{proj}\of{#1, #2} }
  27
  28 % The ``Automorphism group of'' operator.
  29 \newcommand*{\Aut}[1]{ \operatorname{Aut} \of{{#1}} }
  30
  31 % The ``Lie algebra of'' operator.
  32 \newcommand*{\Lie}[1]{ \operatorname{Lie} \of{{#1}} }
  33
  34 % The ``write a matrix as a big vector'' operator.
  35 \newcommand*{\vectorize}[1]{ \operatorname{vec} \of{{#1}} }
  36
  37 % The ``write a big vector as a matrix'' operator.
  38 \newcommand*{\matricize}[1]{ \operatorname{mat} \of{{#1}} }
  39
  40 % The inverse of the adjoint of an operator (the argument).
  41 \newcommand*{\adjinv}[1]{ \left( {#1}^{*} \right)^{-1} }
  42
  43 % An inline column vector, with parentheses and a transpose operator.
  44 \newcommand*{\colvec}[1]{ \left( {#1} \right)^{T} }