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% Document Info
\author{royqh1979}
\pdfinfo{
  /Title (linear-algebra-using-sympy.pdf)
  /Creator (Cheatography)
  /Author (royqh1979)
  /Subject (Linear Algebra Using SymPy Cheat Sheet)
}

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\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{C}
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    \vspace{-7pt}
    {\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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\begin{tabulary}{11cm}{L}
    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Linear Algebra Using SymPy Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{royqh1979} via \textcolor{DarkBackground}{\uline{cheatography.com/87753/cs/20231/}}}
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\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{LL}
  \SetRowColor{FootBackground}
  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}royqh1979 \\
  \uline{cheatography.com/royqh1979} \\
  \end{tabulary}
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Published 8th August, 2019.\\
   Updated 24th August, 2019.\\
   Page {\thepage} of \pageref{LastPage}.
\end{tabulary}
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  %\includegraphics[width=48px,height=48px]{dave.jpeg}
  Measure your website readability!\\
  www.readability-score.com
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\end{multicols}}




\begin{document}
\raggedright
\raggedcolumns

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% from this page to resize cheat sheet text:
% www.emerson.emory.edu/services/latex/latex_169.html
\footnotesize % Small font.

\begin{multicols*}{3}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Import SymPy}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{import sympy as sp% Row Count 1 (+ 1)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{2.63781 cm} x{2.33919 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Matrix Creation}}  \tn
% Row 0
\SetRowColor{LightBackground}
normal Matrix & sp.{\bf{Matrix}}({[}{[}1,2{]},{[}3,4{]}{]}) \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
Matrix with all zeros & sp.{\bf{zeros}}(4,5) \tn 
% Row Count 3 (+ 1)
% Row 2
\SetRowColor{LightBackground}
Matrix with all ones & sp.{\bf{ones}}(4,5) \tn 
% Row Count 4 (+ 1)
% Row 3
\SetRowColor{white}
Square matrix with all zeros & sp.{\bf{zeros}}(5) \tn 
% Row Count 6 (+ 2)
% Row 4
\SetRowColor{LightBackground}
Square matrix with all ones & sp.{\bf{ones}}(5) \tn 
% Row Count 8 (+ 2)
% Row 5
\SetRowColor{white}
Identity matrix & sp.{\bf{eyes}}(5) \tn 
% Row Count 9 (+ 1)
% Row 6
\SetRowColor{LightBackground}
Diagonal Matrix & sp.{\bf{diag}}(1,2,3,4) \tn 
% Row Count 11 (+ 2)
% Row 7
\SetRowColor{white}
Generate element with func(i,j) & sp.{\bf{Matrix}}(2,3,func) \tn 
% Row Count 13 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{2.93643 cm} x{2.04057 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Matrix Modification}}  \tn
% Row 0
\SetRowColor{LightBackground}
Delete the i-th row & M.row\_del(i) \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
Delete the j-th column & M.col\_del(j) \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
Row join M1 and M2 & M1.row\_join(M2) \tn 
% Row Count 3 (+ 1)
% Row 3
\SetRowColor{white}
Column join M1 and M2 & M1.col\_join(M2) \tn 
% Row Count 4 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{3.93183 cm} x{1.04517 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Indexing(Slicing)}}  \tn
% Row 0
\SetRowColor{LightBackground}
get the element in M at (i,j) & M{[}i,j{]} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
get the i-th row in M & \seqsplit{M.row(i)} \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
get the i-th row in M & M{[}i,:{]} \tn 
% Row Count 3 (+ 1)
% Row 3
\SetRowColor{white}
get the j-th column in M & \seqsplit{M.col(j)} \tn 
% Row Count 4 (+ 1)
% Row 4
\SetRowColor{LightBackground}
get the j-th column in M & M{[}:,j{]} \tn 
% Row Count 5 (+ 1)
% Row 5
\SetRowColor{white}
get the i-th and the k-th rows & M{[}{[}i,k{]},:{]} \tn 
% Row Count 7 (+ 2)
% Row 6
\SetRowColor{LightBackground}
get the j-th and the k-th columns & M{[}:,{[}j,k{]}{]} \tn 
% Row Count 9 (+ 2)
% Row 7
\SetRowColor{white}
get rows from i to k & M{[}i:k,:{]} \tn 
% Row Count 10 (+ 1)
% Row 8
\SetRowColor{LightBackground}
get columns from j to k & M{[}:,j:k{]} \tn 
% Row Count 11 (+ 1)
% Row 9
\SetRowColor{white}
get sub-matrix (row i to k,col j to l) & M{[}i:k,j:l{]} \tn 
% Row Count 13 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{{\bf{Note}}: All indices start from 0}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{1.74195 cm} x{3.23505 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Basic opertaions}}  \tn
% Row 0
\SetRowColor{LightBackground}
Sum & A+B \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
Substraction & A-B \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
Matrix Multiply & A*B \tn 
% Row Count 4 (+ 2)
% Row 3
\SetRowColor{white}
Scalar Multiply & 5*A \tn 
% Row Count 6 (+ 2)
% Row 4
\SetRowColor{LightBackground}
Elementwise product & \seqsplit{sp.matrix\_multiply\_elementwise(A},B) \tn 
% Row Count 8 (+ 2)
% Row 5
\SetRowColor{white}
Transpose & A.T \tn 
% Row Count 9 (+ 1)
% Row 6
\SetRowColor{LightBackground}
Determinant & A.det() \tn 
% Row Count 10 (+ 1)
% Row 7
\SetRowColor{white}
Inverse & A.inv() \tn 
% Row Count 11 (+ 1)
% Row 8
\SetRowColor{LightBackground}
Condition Number & A.condition\_number() \tn 
% Row Count 13 (+ 2)
% Row 9
\SetRowColor{white}
Row count & A.rows \tn 
% Row Count 14 (+ 1)
% Row 10
\SetRowColor{LightBackground}
Column count & A.cols \tn 
% Row Count 15 (+ 1)
% Row 11
\SetRowColor{white}
Trace & A.trace() \tn 
% Row Count 16 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{1.09494 cm} x{3.88206 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Elementary Row Operations}}  \tn
% Row 0
\SetRowColor{LightBackground}
\seqsplit{Replacement} & m.row\_op(i, {\bf{lambda}} ele,col:ele+m.row(j){[}col{]}*c) \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
\seqsplit{Interchange} & M.row\_swap(i,j) \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
Scaling & m.row\_op(i,{\bf{lambda}} ele,col:ele*c) \tn 
% Row Count 6 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{2.33919 cm} x{2.63781 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Linear Equations}}  \tn
% Row 0
\SetRowColor{LightBackground}
Echelon From & M.echelon\_form() \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
Reduced Echelon Form & M.rref() \tn 
% Row Count 3 (+ 2)
% Row 2
\SetRowColor{LightBackground}
Solve AX=B (B can be a matrix) & x,freevars=A.gauss\_jordan\_solve(B) \tn 
% Row Count 5 (+ 2)
% Row 3
\SetRowColor{white}
least-square fit Ax=b & \seqsplit{A.solve\_least\_squares(b)} \tn 
% Row Count 7 (+ 2)
% Row 4
\SetRowColor{LightBackground}
solve Ax=b & A.solve(b) \tn 
% Row Count 8 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{2.88666 cm} x{2.09034 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Vector Space}}  \tn
% Row 0
\SetRowColor{LightBackground}
Basis of column space & M.columnspace() \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
Basis of null space & M.nullspace() \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
Basis of row space & M.rowspace() \tn 
% Row Count 3 (+ 1)
% Row 3
\SetRowColor{white}
Rank & M.rank() \tn 
% Row Count 4 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{3.23505 cm} x{1.74195 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Eigenvalues amd Eigenvectors}}  \tn
% Row 0
\SetRowColor{LightBackground}
Find the eigenvalues & M.eigenvals() \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
Find the eignevalues and the corresponding eigenspace & \seqsplit{M.eigenvects()} \tn 
% Row Count 4 (+ 3)
% Row 2
\SetRowColor{LightBackground}
Diagonalize a matrix & P, D = \seqsplit{M.diagonalize()} \tn 
% Row Count 6 (+ 2)
% Row 3
\SetRowColor{white}
test if the matrix is diagonalizable & \seqsplit{M.is\_diagonalizable} \tn 
% Row Count 8 (+ 2)
% Row 4
\SetRowColor{LightBackground}
Calculate Jordan From & P, J = \seqsplit{M.jordan\_form()} \tn 
% Row Count 10 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{2.38896 cm} x{2.58804 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Decomposition}}  \tn
% Row 0
\SetRowColor{LightBackground}
LU \seqsplit{Decomposition(PA=LU)} & P,L,U=A.LUdecomposition() \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
QR Decomposition & Q,R=A.QRdecomposition() \tn 
% Row Count 4 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{2.78712 cm} x{2.18988 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Vector Operations}}  \tn
% Row 0
\SetRowColor{LightBackground}
Create a column vector & v=sp.Matrix({[}1,2,3{]}) \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
dot product & v1.dot(v2) \tn 
% Row Count 3 (+ 1)
% Row 2
\SetRowColor{LightBackground}
cross product & v1.cross(v2) \tn 
% Row Count 4 (+ 1)
% Row 3
\SetRowColor{white}
length of the vector & v.norm() \tn 
% Row Count 5 (+ 1)
% Row 4
\SetRowColor{LightBackground}
normalize of vector & v.normalize() \tn 
% Row Count 6 (+ 1)
% Row 5
\SetRowColor{white}
the projection of v1 on v2 & v1.project(v2) \tn 
% Row Count 8 (+ 2)
% Row 6
\SetRowColor{LightBackground}
Gram-Schmidt orthogonalize & sp.GramSchmidt({[}v1,v2,v3{]}) \tn 
% Row Count 10 (+ 2)
% Row 7
\SetRowColor{white}
Gram-Schmidt orthogonalize with normalization & sp.GramSchmidt({[}v1,v2,v3{]},True) \tn 
% Row Count 13 (+ 3)
% Row 8
\SetRowColor{LightBackground}
Singular values & \seqsplit{M.singlular\_values()} \tn 
% Row Count 15 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{2.43873 cm} x{2.53827 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Block Matrix}}  \tn
% Row 0
\SetRowColor{LightBackground}
Create a  matrix by block & M=sp.Matrix({[}{[}A,B{]},{[}C,D{]}{]}) \tn 
% Row Count 2 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Useful Links}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{\{\{link="https://docs.sympy.org/latest/modules/matrices/matrices.html\#"\}\}SymPy Documentation\{\{/link\}\}} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{\{\{link="https://docs.sympy.org/latest/tutorial/matrices.html\#"\}\}SymPy Tutorial\{\{/link\}\}} \tn 
% Row Count 4 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}


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

\end{document}