On a theorem of de Bruijn and Erdös

Abstract A theorem of de Bruijn and Erdos [2] asserts that every finite geometry (see section 1 for definition) has at least as many lines as points. The present paper uses linear algebra as a technique to establish the de Bruijn-Erdos result and a particular higher dimensional generalization. These results are special cases of theorems due to Basterfield and Kelly [1] and Green [3].