A measure concentration effect for matrices of high, higher, and even higher dimension

Harry Yserentant

Let $n>m$, and let $A$ be an $(m\times n)$-matrix of full rank. Then obviously the estimate $\Vert Ax\Vert \le \Vert A\Vert \Vert x\Vert$ holds for the euclidean norm of $x$ and $Ax$ and the spectral nor…