Some properties complementary to Brualdi-Li matrices
In this paper we derive new properties complementary to an Brualdi-Li tournament matrix . We show that has exactly one positive real eigenvalue and one negative real eigenvalue and, as a by-product, reprove that every Brualdi-Li matrix has distinct eigenvalues. We then bound the partial sums of the real parts and the imaginary parts of its eigenvalues. The inverse of is also determined. Related results obtained in previous articles are proven to be corollaries.