Skip to main content\(\newcommand{\avec}{{\boldsymbol a}}
\newcommand{\bvec}{{\boldsymbol b}}
\newcommand{\cvec}{{\boldsymbol c}}
\newcommand{\dvec}{{\boldsymbol d}}
\newcommand{\dtil}{\widetilde{\boldsymbol d}}
\newcommand{\evec}{{\boldsymbol e}}
\newcommand{\fvec}{{\boldsymbol f}}
\newcommand{\mvec}{{\boldsymbol m}}
\newcommand{\nvec}{{\boldsymbol n}}
\newcommand{\pvec}{{\boldsymbol p}}
\newcommand{\qvec}{{\boldsymbol q}}
\newcommand{\rvec}{{\boldsymbol r}}
\newcommand{\svec}{{\boldsymbol s}}
\newcommand{\tvec}{{\boldsymbol t}}
\newcommand{\uvec}{{\boldsymbol u}}
\newcommand{\vvec}{{\boldsymbol v}}
\newcommand{\wvec}{{\boldsymbol w}}
\newcommand{\xvec}{{\boldsymbol x}}
\newcommand{\yvec}{{\boldsymbol y}}
\newcommand{\zvec}{{\boldsymbol z}}
\newcommand{\betavec}{{\boldsymbol \beta}}
\newcommand{\E}{\operatorname{E}}
\newcommand{\zerovec}{{\boldsymbol 0}}
\newcommand{\onevec}{{\boldsymbol 1}}
\newcommand{\real}{{\mathbb R}}
\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2
\end{array}\right]}
\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2
\end{array}\right]}
\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3
\end{array}\right]}
\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3
\end{array}\right]}
\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4
\end{array}\right]}
\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4
\end{array}\right]}
\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\
#4 \\ #5 \\ \end{array}\right]}
\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\
#4 \\ #5 \\ \end{array}\right]}
\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}
\newcommand{\laspan}[1]{\text{Span}\{#1\}}
\newcommand{\bcal}{{\cal B}}
\newcommand{\ccal}{{\cal C}}
\newcommand{\scal}{{\cal S}}
\newcommand{\wcal}{{\cal W}}
\newcommand{\ecal}{{\cal E}}
\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}
\newcommand{\gray}[1]{\color{gray}{#1}}
\newcommand{\lgray}[1]{\color{lightgray}{#1}}
\newcommand{\rank}{\operatorname{rank}}
\newcommand{\row}{\text{Row}}
\newcommand{\col}{\text{Col}}
\renewcommand{\row}{\text{Row}}
\newcommand{\nul}{\text{Nul}}
\newcommand{\var}{\text{Var}}
\newcommand{\cov}{\text{Cov}}
\newcommand{\corr}{\text{corr}}
\newcommand{\len}[1]{\left|#1\right|}
\newcommand{\bbar}{\overline{\bvec}}
\newcommand{\bhat}{\widehat{\bvec}}
\newcommand{\bperp}{\bvec^\perp}
\newcommand{\atilde}{\tilde{\avec}}
\newcommand{\btilde}{\tilde{\bvec}}
\newcommand{\vhat}{\widehat{\vvec}}
\newcommand{\uhat}{\widehat{\uvec}}
\newcommand{\what}{\widehat{\wvec}}
\newcommand{\xhat}{\widehat{\xvec}}
\newcommand{\xmean}{\overline{\xvec}}
\newcommand{\xbar}{\overline{\xvec}}
\newcommand{\xtilde}{\tilde{\xvec}}
\newcommand{\Xtilde}{\tilde{X}}
\newcommand{\yhat}{\widehat{\yvec}}
\newcommand{\ymean}{\overline{\yvec}}
\newcommand{\ybar}{\overline{\yvec}}
\newcommand{\ytilde}{\tilde{\yvec}}
\newcommand{\yperp}{\yvec^\perp}
\newcommand{\betahat}{\widehat{\betavec}}
\newcommand{\Sighat}{\widehat{\Sigma}}
\newcommand{\by}{\times}
\newcommand{\transpose}{\top}
\newcommand{\proj}[2]{\operatorname{proj}\left(#1 \to #2\right)}
\newcommand{\projsub}[2]{\operatorname{proj}_{#2}(#1)}
\newcommand{\lt}{<}
\newcommand{\gt}{>}
\newcommand{\amp}{&}
\definecolor{fillinmathshade}{gray}{0.9}
\newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}}
\)
Subsection B.1 Accessing Python
In addition to the SageMath cellls included throughout the book, there are a number of ways to access Python. Here are just a few.
You can save your Sage work by creating an account at
cocalc.com and working in a Sage worksheet.
For createing documents that include Python code, jupter notebooks, or quarto documents work well.
VS Code can be configured to not only edit, but also execute Python code (and jupyter notebooks and quarto documents)
