Abstract
Given n-square Hermitian matrices A, B, let A i , B i denote the principal ( n−1)- square submatrices of A, B, respectively, obtained by deleting row i and column i. Let μ, λ be independent indeterminates. The first main result of this paper is the characterization (for fixed i) of the polynomials representable as det(μ A i−λ B i) in terms of the polynomial det(μ A−λ B) and the elementary divisors, minimal indices, and inertial signatures of the pencil μ A−λ B. This result contains, as a special case, the classical interlacing relationship governing the eigenvalues of a principal sub- matrix of a Hermitian matrix. The second main result is the determination of the number of different values of i to which the characterization just described can be simultaneously applied.
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