ELA, Volume 13, pp. 157-161, June 2005, abstract.
On a Conjecture Regarding Characteristic Polynomial
of a Matrix Pair
C.M. da Fonseca
For n-by-n Hermitian matrices A (>0) and B, define
eta(A,B)=sum det A(S) det B(S'), where the summation
is over all subsets of {1,...,n}, S' is the complement
of S, and by convention det A(emptyset)=1. Bapat proved
for n=3 that the zeros of eta(lambda A,-B) and the zeros
of eta(lambda A(23),-B(23)) interlace. This result is
generalized to a broader class of matrices.