Let $n>m$, and let $A$ be an $(m\times n)$-matrix of full rank. Then obviously the estimate $\|Ax\|\leq\|A\|\|x\|$ holds for euclidean norm $x$ $Ax$ spectral as assigned matrix norm. We study sets all which, fixed $\delta<1$, conversely $\|Ax\|\geq\delta\,\|A\|\|x\|$ holds. It turns out that these fill, in high-dimensional case, almost complete space once $\delta$ falls below a bound depends on...