In “The Theory of Matrices” by Gantmacher, Chapter II, section 4: Corollary $ 3$ : If $ S= ||s_{ik}||_1^n$ is a symmetric matrix of rank $ r$ and $ $ D_k= S\bigl( \begin{smallmatrix} 1 & 2 & \dots & k \ 1 & 2 & \dots & k \end{smallmatrix} \bigr)\ne 0 \ \ \ \Read more