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\(\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\,}$}}} \)

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Edition 2023 Data Science Edition

Website ula-ds.netlify.com

This work is licensed under a Creative Commons Attribution 4.0 International License ¹.

Understanding Linear Algebra was written and is maintained by David Austin. It can be found at https://davidaustinm.github.io/ula/home.html

Understading Linear Algebra for Data Science is a derived version. Differences to the original include the use of Python (with the numpy and sympy packages) rather than Sage, and some additional emphasis on data science topics.

creativecommons.org

Understanding Linear Algebra: Data Science Edition

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