I was looking around for a table detailing the difference in solving / approximating linear systems in under- and over-determined cases but didn't find anything that summarized the cases nicely. I'm trying to fill out the following table for use as a teaching / studying device and have pulled in some details from Wikipedia etc. Any additions / suggestions would be appreciated!
Sorry for the poor formatting (I've included LaTex code below).
\documentclass[12pt]{beamer}
\usepackage{pdfpages}
\usepackage{booktabs} % subfigure / table stuff
\usepackage{siunitx} % table stuff
\begin{document}
\begin{frame}
\tiny
Linear Systems Summary: $A \in \mathbb{R}^{m \times n}$, $x \in \mathbb{R}^n$, and $b \in \mathbb{R}^m$
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\begin{table}
\begin{tabular}{@{} *7l @{}}
\toprule
\emph{type} & \emph{size} & \emph{case} & \emph{rank(A)} & \emph{true solns} & \emph{$A^\dagger$ soln} &\emph{comments} \\ \midrule
Overdetermined & $m>n$ & $b \not \in \mathcal{R}(A)$ & full col & none & $\min \norm{Ax - b}_2^2$ & ``least-squares'' \\
& & & & (inconsistent) & & problem \\
\hline
Overdetermined & $m>n$ & $b \not \in \mathcal{R}(A)$ & $n$ & $b \in \mathcal{R}(A)$ & & & & \\
\hline
Underdetermined & $m