Nonnegative alternating circulants leading to M-matrix group inverses Original Research Article

Let image be the set of all an n × n nonnegative irreducible alternating circulant matrices. We characterize a subset image of image such that if B set membership, variant C and the Perron root of B is r, then the group inverse (rI − B)# of the singular and irreducible M-matrixrI − B is also an M-matrix. This is equivalent to the fact that for each such B, the Perron root at B is a concave function in each of the off-diagonal entries. The characterization for the case when n is odd presents more difficulties than for the case when n is even, so the two cases are treated separately.