The structure matrix of (0,1)-matrices: Its rank, trace, and eigenvalues. An application to econometric models

AbstractThis paper deals with questions raised by R.A. Brualdi concerning the structure matrix of (0,1)-matrices with fixed row and column sum vectors; namely, determining its rank and—in case the matrices are square—its eigenvalues. It turns out that the trace of the structure matrix has some interesting properties. The rank of the structure matrix has the values 1,2, or 3; this yields a classification of econometric models