X-Git-Url: http://gitweb.michael.orlitzky.com/?p=mjotex.git;a=blobdiff_plain;f=mjo-linear_algebra.tex;h=5c3f715744b14db7b4984b063952f02ba5ac530e;hp=048022935b681bfe5f0d0c04366f7fadcb6383d2;hb=7321e6c665f3b9797bb7a76618e6419a33357e6c;hpb=5c4f67545f0988d065f1d52f90eed9233562c9fc diff --git a/mjo-linear_algebra.tex b/mjo-linear_algebra.tex index 0480229..5c3f715 100644 --- a/mjo-linear_algebra.tex +++ b/mjo-linear_algebra.tex @@ -37,6 +37,10 @@ % specialized to real matrices. \newcommand*{\transpose}[1]{ #1^{T} } +% The Moore-Penrose (or any other, I guess) pseudo-inverse of its +% sole argument. +\newcommand*{\pseudoinverse}[1]{ #1^{+} } + % The trace of an operator. \newcommand*{\trace}[1]{ \operatorname{trace}\of{{#1}} } @@ -62,7 +66,7 @@ \newcommand*{\matricize}[1]{ \operatorname{mat}\of{{#1}} } % An inline column vector, with parentheses and a transpose operator. -\newcommand*{\colvec}[1]{ \left({#1}\right)^{T} } +\newcommand*{\colvec}[1]{ \transpose{\left({#1}\right)} } % Bounded linear operators on some space. The required argument is the % domain of those operators, and the optional argument is the @@ -89,7 +93,7 @@ \DeclareMathOperator{\oplusperp}{\mathbin{ \ooalign{ $\ocircle$\cr - \raisebox{0.65\height}{$\clipbox{0pt 0pt 0pt 0.5\height}{$\perp$}$}\cr + \raisebox{0.625\height}{$\clipbox{0pt 0pt 0pt 0.5\height}{$\perp$}$}\cr } }}