
details
Author(s)
Carlos Fonseca;
Title On a conjecture regarding characteristic polynomial of a matrix pair
Abstract For $n$by$n$ Hermitian matrices $A(>0)$ and $B$, define
$$\eta(A,B)=\sum_S\det A(S)\det B(S^\prime \; ,$$ where the summation is over all subsets of $\{1,\ldots,n\}$, $S^\prime$ is
the complement of $S$, and by convention $\det A(\emptyset)=\det B(\emptyset)=1$. Bapat proved for $n=3$ that the zeros of $\eta(\lambda A,B)$ and the zeros of $\eta(\lambda A(23),B(23))$ interlace. We generalize this result to a broader class of
matrices.
Journal Electronic Journal of Linear Algebra
Volume 13
Year 2005
Issue
Page(s) 157161

