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Course: Math 535 - Mathematical Methods in Data Science (MMiDS) Chapter: 2-Least squares: geometric, algebraic, and numerical aspects Author: Sebastien Roch , Department of Mathematics, University of Wisconsin-Madison Updated: July 15, 2024 Copyright: © 2024 Sebastien Roch $\newcommand{\bmu}{\boldsymbol{\mu}}$ $\newcommand{\bSigma}{\boldsymbol{\Sigma}}$ $\newcommand{\bfbeta}{\boldsymbol{\beta}}$ $\newcommand{\bflambda}{\boldsymbol{\lambda}}$ $\newcommand{\bgamma}{\boldsymbol{\gamma}}$ $\newcommand{\bsigma}{{\boldsymbol{\sigma}}}$ $\newcommand{\bpi}{\boldsymbol{\pi}}$ $\newcommand{\btheta}{{\boldsymbol{\theta}}}$ $\newcommand{\bphi}{\boldsymbol{\phi}}$ $\newcommand{\balpha}{\boldsymbol{\alpha}}$ $\newcommand{\blambda}{\boldsymbol{\lambda}}$ $\renewcommand{\P}{\mathbb{P}}$ $\newcommand{\E}{\mathbb{E}}$ $\newcommand{\indep}{\perp\!\!\!\perp} \newcommand{\bx}{\mathbf{x}}$ $\newcommand{\bp}{\mathbf{p}}$ $\renewcommand{\bx}{\mathbf{x}}$ $\newcommand{\bX}{\mathbf{X}}$ $\newcommand{\by}{\mathbf{y}}$ $\newcommand{\bY}{\mathbf{Y}}$ $\newcommand{\bz}{\mathbf{z}}$ $\newcommand{\bZ}{\mathbf{Z}}$ $\newcommand{\bw}{\mathbf{w}}$ $\newcommand{\bW}{\mathbf{W}}$ $\newcommand{\bv}{\mathbf{v}}$ $\newcommand{\bV}{\mathbf{V}}$ $\newcommand{\bfg}{\mathbf{g}}$ $\newcommand{\bfh}{\mathbf{h}}$ $\newcommand{\horz}{\rule[.5ex]{2.5ex}{0.5pt}}$ $\renewcommand{\S}{\mathcal{S}}$ $\newcommand{\X}{\mathcal{X}}$ $\newcommand{\var}{\mathrm{Var}}$ $\newcommand{\pa}{\mathrm{pa}}$ $\newcommand{\Z}{\mathcal{Z}}$ $\newcommand{\bh}{\mathbf{h}}$ $\newcommand{\bb}{\mathbf{b}}$ $\newcommand{\bc}{\mathbf{c}}$ $\newcommand{\cE}{\mathcal{E}}$ $\newcommand{\cP}{\mathcal{P}}$ $\newcommand{\bbeta}{\boldsymbol{\beta}}$ $\newcommand{\bLambda}{\boldsymbol{\Lambda}}$ $\newcommand{\cov}{\mathrm{Cov}}$ $\newcommand{\bfk}{\mathbf{k}}$ $\newcommand{\idx}[1]{}$ $\newcommand{\xdi}{}$