%
% linalg2270strang.sty
%
%
% Special symbols
%
\def\L{{\cal L}}
\def\dd{\displaystyle}
\def\cents{\hbox{\rm\rlap/c}}
\def\Cos{\mathop{\bf Cos}\nolimits}
%\newcommand{\choose}[2]{\left(\begin{array}{r} #1 \\ #2 \end{array}\right)}
%\long\def\choose#1#2{\left(\begin{array}{r} #1 \\ #2 \end{array}\right)}
\def\div{\mathop{\bf div}\nolimits}
\def\RR{{\bf R}}
\def\CC{{\bf C}}
\def\Nn{{\cal N}}
\def\Rr{{\cal R}}
\def\adjoint{\mathop{\bf adjoint}\nolimits}
\def\AUG{\mathop{\bf aug}\nolimits}
\def\nullity{\mathop{\bf nullity}\nolimits}
\newcommand{\aug}[2]{\left(#1\,:\,#2\right)}
%\def\aug#1#2{\left(#1\,:\,#2\right)}
\def\BF#1{{\bf #1}}
\def\FF{\mbox{\fbox{$1$}}}
\def\erf{\mathop{\bf erf}\nolimits}
\def\rref{\mathop{\bf rref}\nolimits}
\def\grad{\mathop{\bf grad}\nolimits}
\def\rank{\mathop{\bf rank}\nolimits}
% Define \WRAPFIG{\AA}{\BB}{1.0in} for wrapping text /w figures.
%        This puts \AA on the left, \BB on the right in box width \DIM
% Usage: \def\DIM{1.0in}\def\AA{...}\def\BB{...}
%        \WRAPFIG{\AA}{\BB}{\DIM}
%
\newdimen\miniFIGwidth
\newdimen\miniTXTwidth
%\long\def\WRAPFIG#1#2#3{%
\newcommand{\WRAPFIG}[3]{%
\miniFIGwidth=#3\relax
\miniTXTwidth=\hsize\relax
\addtolength{\miniTXTwidth}{-\miniFIGwidth}
\addtolength{\miniTXTwidth}{-0.3in}
\begin{tabular}{@{}p{\miniTXTwidth}@{\hspace{0.1in}}p{\miniFIGwidth}}%
\begin{minipage}{\miniTXTwidth}%
#1
\end{minipage} &
\begin{minipage}{\miniFIGwidth}%
#2
\end{minipage}
\end{tabular}%
}
%
% Linear algebra definitions for matrices and vectors.
%
\def\cof{\mathop{\bf cof}\nolimits}
\def\adj{\mathop{\bf adj}\nolimits}
\def\SPAN{\mathop{\bf span}\nolimits}
%\def\augment#1#2{\left(#1\,:\,#2\right)}
\newcommand{\WORKUP}[1]{
\begin{tabular}{@{}p{2.4in}p{1.0in}}
#1
\end{tabular}
}
%\newcommand{\.}[1]{\mbox{\bf #1}}
\def\diag{\mathop{\bf diag}\nolimits}
\def\cof{\mathop{\bf cof}\nolimits}
\def\adj{\mathop{\bf adj}\nolimits}
%\def\augment#1#2{\left(#1\,:\,#2\right)}

\long\def\WORKUP#1{
\begin{tabular}{@{}p{2.4in}p{1.0in}}
#1
\end{tabular}
}

\def\.#1{\mbox{\bf #1}}
\def\diag{\mathop{\bf diag}\nolimits}

\long\def\colvector#1{\left(\begin{array}{r}#1\end{array}\right)}
\long\def\colvectorC#1{\left(\begin{array}{c}#1\end{array}\right)}
\long\def\minicolvector#1{\left(\begin{array}{@{}r@{}}#1\end{array}\right)}
\long\def\minicolvectorC#1{\left(\begin{array}{@{}c@{}}#1\end{array}\right)}
\long\def\rowvector#1{\left(\!\begin{array}{llllll}#1\end{array}\!\right)}
\long\def\rowvectorC#1{\left(\!\begin{array}{cccccc}#1\end{array}\!\right)}
\def\twobytwo#1#2{%
\left(\begin{array}{rr}
#1 \\ #2
\end{array}\right)
}
\def\threebythree#1#2#3{%
\left(\begin{array}{rrr}
#1 \\ #2 \\ #3
\end{array}\right)
}
\def\fourbyfour#1#2#3#4{%
\left(\begin{array}{rrrr}
#1 \\ #2 \\ #3 \\ #4
\end{array}\right)
}
\def\fivebyfive#1#2#3#4#5{%
\left(\begin{array}{rrrrr}
#1 \\ #2 \\ #3 \\ #4 \\ #5
\end{array}\right)
}
\def\minitwobytwo#1#2{%
\left(\begin{array}{@{}r@{\hspace{0.6ex}}r@{}}
#1 \\[-0.75ex] #2
\end{array}\right)
}
\def\minitwobytwoC#1#2{%
\left(\begin{array}{@{}c@{\hspace{0.6ex}}c@{}}
#1 \\[-0.75ex] #2
\end{array}\right)
}
\def\minithreebythree#1#2#3{%
\left(\begin{array}{@{}r@{\hspace{0.6ex}}r@{\hspace{0.6ex}}r@{}}
#1 \\ #2 \\ #3
\end{array}\right)
}
\def\minifourbyfour#1#2#3#4{%
\left(\begin{array}{@{}r@{\hspace{0.6ex}}r@{\hspace{0.6ex}}r@{\hspace{0.6ex}}r@{}}
#1 \\ #2 \\ #3 \\ #4
\end{array}\right)
}
\def\minifivebyfive#1#2#3#4#5{%
\left(\begin{array}{@{}r@{\hspace{0.6ex}}r@{\hspace{0.6ex}}r@{\hspace{0.6ex}}r@{\hspace{0.6ex}}r@{}}
#1 \\ #2 \\ #3 \\ #4 \\ #5
\end{array}\right)
}
\def\minisixbysix#1#2#3#4#5#6{%
\left(\begin{array}{@{}r@{\hspace{0.6ex}}r@{\hspace{0.6ex}}r@{\hspace{0.6ex}}r@{\hspace{0.6ex}}r@{\hspace{0.6ex}}r@{}}
#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ #6
\end{array}\right)
}
\def\Threebythree#1#2#3{%
\left(\begin{array}{@{}r@{\hspace{0.6ex}}r@{\hspace{0.6ex}}r@{}} #1 \\ #2 \\
#3
\end{array}\right)
}
\def\DETtwobytwo#1#2{%
\left|\begin{array}{rr}
#1 \\ #2
\end{array}\right|
}\def\DETthreebythree#1#2#3{%
\left|\begin{array}{rrr}
#1 \\ #2 \\ #3
\end{array}\right|
}
\def\DETfourbyfour#1#2#3#4{%
\left|\begin{array}{rrrr}
#1 \\ #2 \\ #3 \\ #4
\end{array}\right|
}
\def\DETminitwobytwo#1#2{%
\left|\begin{array}{@{}r@{\hspace{0.6ex}}r@{}}
#1 \\[-0.75ex] #2
\end{array}\right|
}
\def\DETminithreebythree#1#2#3{%
\left|\begin{array}{@{}r@{\hspace{0.6ex}}r@{\hspace{0.6ex}}r@{}}
#1 \\ #2 \\ #3
\end{array}\right|
}
\def\DETminifourbyfour#1#2#3#4{%
\left|\begin{array}{@{}r@{\hspace{0.6ex}}r@{\hspace{0.6ex}}r@{\hspace{0.6ex}}r@{}}
#1 \\ #2 \\ #3 \\ #4
\end{array}\right|
}
