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 details Author(s) Carlos Fonseca; TitleOn a conjecture regarding characteristic polynomial of a matrix pair AbstractFor $n$-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 Volume13 Year2005 Issue Page(s)157-161 CMUC Apartado 3008, 3001 - 454 Coimbra, Portugal T:+351 239 791 150 F:+351 239 793 069 cmuc@mat.uc.pt - developed by Flor de Utopia