Invertibility of the base Radon transform of a matroid (Q1201244)

Let \(M\) be a matroid of rank \(r\) on \(n\) elements and let \(F\) be a field with characteristic either zero or greater than \(r\). The point-base incidence matrix of \(M\) is shown to have rank \(n-k+1\) over \(F\), where \(k\) is the number of connected components of \(M\). This implies results on the invertibility of the Radon transform on the family of bases (or \(m\)- element independent sets) of \(M\).