From the authors’ abstract: Let an \(m\times n\) matrix \(A\) be approximated by a rank-\(r\) matrix with an accuracy \(\varepsilon\). The paper presents a proof that it is possible to choose \(r\) columns and \(r\) rows of \(A\) forming a so-called pseudoskeleton component which approximates \(A\) with \({\mathcal O}(\varepsilon\sqrt r(\sqrt m+\sqrt n))\) accuracy in the sense of the 2-norm. On the way to this estimate a study concerning the interconnection between the volume (i.e., the determinant in the absolute value) and the minimal singular value \(\sigma_r\) of \(r\times r\) submatrices of an \(n\times r\) matrix with orthogonal columns is presented. Furthermore, the authors propose a lower bound for the maximum of \(\sigma_r\) over all these submatrices and formulate a hypothesis on a tighter bound.