On the Extrema of Linear Least-Squares Problems

We use the concept of generalized inverses to show that the extrema of the function \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G(x) = \|Ax-b\|^2$$\end{document} are minima, A being a rectangular matrix not necessarily of full rank