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\,}$}}}
\)
Understanding Linear Algebra: Data Science Edition
November 26, 2023
