The following is a question from the book.
I’ve understood and solved part a) using the Cauchy-Schwarz inequality. However I don’t understand part b). I know it has something to do with the Banach’s fixed point theorem, since it’s a contraction in an Euclidean space. I request you to shed some light on this part.
$Mx+m=0 \iff cMx + cm= 0 \iff x-cMx-cm = x \iff Ax -cm = x$.
Hence $x$ is a solution if and only if it is a fixed point of $x\mapsto Ax-cm$, which is a contraction because ...