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\author{spoopyy}
\pdfinfo{
  /Title (linear-algebra.pdf)
  /Creator (Cheatography)
  /Author (spoopyy)
  /Subject (Linear Algebra Cheat Sheet)
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    {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent
        \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}}
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    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Linear Algebra Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{spoopyy} via \textcolor{DarkBackground}{\uline{cheatography.com/28376/cs/8341/}}}
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\noindent
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  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}spoopyy \\
  \uline{cheatography.com/spoopyy} \\
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Published 4th June, 2016.\\
   Updated 4th June, 2016.\\
   Page {\thepage} of \pageref{LastPage}.
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  %\includegraphics[width=48px,height=48px]{dave.jpeg}
  Measure your website readability!\\
  www.readability-score.com
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\mymulticolumn{1}{x{3.833cm}}{a set of vectors S is	LI if	c1v1	+...+	ckvk	= 0 has only the trivial solution.  \newline % Row Count 2 (+ 2)
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\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{Nullity}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{3.833cm}}{Nullspace(A)	=	\{x	ε R\textasciicircum{}n\textasciicircum{} :	Ax	=	0 \newline % Row Count 1 (+ 1)
\seqsplit{Nullity(A)	=	dim(Nullspace(A))	} \newline % Row Count 2 (+ 1)
=	n	- rank(A)% Row Count 3 (+ 1)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{3.833cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{Orthogonal Sets}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{3.833cm}}{\seqsplit{Set	S	in	V	is	orthogonal	when	every	pair	of	vectors} in \seqsplit{S	is	orthogonal.	If	each	} vector	is	a	unit	vector, then	S	is	orthonormal% Row Count 3 (+ 3)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{3.833cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{One-to-One and	Onto}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{3.833cm}}{T	is	one-to-one	{\bf{iff}}	ker(T)	=	\{0\}} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{3.833cm}}{T	is	onto	{\bf{iff}}	rank(T)	=	dim(W)} \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{3.833cm}}{If	dim(T)	=	dim(W) then	T	is	one-to-one	{\bf{iff}}	it	is	onto} \tn 
% Row Count 4 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{3.833cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{Rank	and	Nullity	of	T}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{3.833cm}}{nullity(T)	=	dim(kernal)} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{3.833cm}}{rank(T)	=	dim(range)} \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{3.833cm}}{\seqsplit{range(T)	+	nullity(T)	=	n	(in	m\_x} n)} \tn 
% Row Count 3 (+ 1)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{3.833cm}}{\seqsplit{dim(domain)	=	dim(range)	+	dim(kernal)}} \tn 
% Row Count 4 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{3.833cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{Rank of a Matrix}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{3.833cm}}{\seqsplit{Rank(A)	=	dim(Rspace)	=	dim(Cspace)}% Row Count 1 (+ 1)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{3.833cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{Similar Matrices}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{3.833cm}}{\seqsplit{For	square	matrices	A	and	A'	of	order	n},	A'	is	similar \seqsplit{to	A	when	there	exits	an	invertible	matrix	P	such	that	A'	=} P\textasciicircum{}-1\textasciicircum{} AP% Row Count 3 (+ 3)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{3.833cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{Spanning Sets}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{3.833cm}}{S	=	\{v1...vk\}	is	a	subset	of	vector	space	V.	S \seqsplit{spans	V	if	every	vector	in	v	can	be	written	as	a	linear} combo	of	vectors	in	S.% Row Count 3 (+ 3)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{3.833cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{Test for Subspace}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{3.833cm}}{1. u+v are in W} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{3.833cm}}{2. cu is in w} \tn 
% Row Count 2 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}


% That's all folks
\end{multicols*}

\end{document}