Geodesic
On a conjecture regarding characteristic polynomial of a matrix pair
The electronic journal of linear algebra, Tome 13 (2005), pp. 157-161.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: For $n$-by-$n$ Hermitian matrices $A\,(>0)$ and $B$, define $$ \eta(A,B)=\sum_S\det A(S)\det B(S'), $$ where the summation is over all subsets of $\{1,\dots,n\}, S'$ 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.
Classification : 15A15, 15A42
Keywords: symmetric matrices, cycles, characteristic polynomial, interlacing 
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     author = {da Fonseca, C.M.},
     title = {On a conjecture regarding characteristic polynomial of a matrix pair},
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da Fonseca, C.M. On a conjecture regarding characteristic polynomial of a matrix pair. The electronic journal of linear algebra, Tome 13 (2005), pp. 157-161. http://geodesic.mathdoc.fr/item/ELA_2005__13__a13/