Algebra and Combinatorics

 

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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)
157-161

 
     
 

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