Author’s abstract: “Let be an \(m\times n\) (0,1)-matrix with row vectors \(R_ 1,...,R_ m\) and column vectors \(C_ 1,...,C_ n\). If there exist integers \(\alpha\),\(\beta\) such hat \(R_ iR_ j=\alpha\) whenever \(R_ i\neq R_ j\) and \(C_ iC_ j=\beta\) whenever \(C_ i\neq C_ j\), then A will be called geometric. \((R_ iR_ j\), \(C_ iC_ j\) are the usual dot products of the vectors involved.) The geometric matrices are classified, and it is shown that (apart from certain trivialities) every geometric matrix is based on a symmetric balanced incomplete block design. Assume that each column of A has a zero entry and that \(C_ i\neq C_ j\) for some i and j. Under these assumptions it is shown that \(m\cdot \min \{R_ iR_ j:R_ i\neq R_ j\}\leq n\cdot \max \{C_ iC_ j:C_ i\neq C_ j\},\) and that equality occurs if and only if A is geometric. The results generalize a theorem of de Bruijn and Erdős concerning combinatorial designs.”