PUB - Publikationen an der Universität Bielefeld

A theorem concerning matroids is proved which—specialized to representable matroids—implies that given a non-singular quadratic n × n-matrix A = (aij) and some k ∈ {1,..., n − 1} such that for any subset S ⊆ {1,..., n} of cardinality k different from {1,..., k}, the product det ((aij)i = 1,...,k; j ∈ S) · det ((aij)i = k + 1,..., n; j ∉ S) in the Laplace expansion of A with respect to the first k and the last n − k rows vanishes, there exists some i ∈ {k + 1,..., n} with a1i = a2i = ⋯ =aki = 0 or some i ∈ {1,..., k) with ak+1,i = ak + 2,i = ⋯ = ani = 0.