Characterization of k-spectrally monomorphic Hermitian matrices
Kawtar Attas, Abderrahim Boussaïri, Imane Souktani · Discrete Mathematics Algorithms and Applications · 2025
This paper solves the following problem about Hermitian matrices related to the theory of [Formula: see text]-structures: Let [Formula: see text] be a positive integer and [Formula: see text] be an integer with [Formula: see text]. Characterize the Hermitian matrices [Formula: see text] such that the characteristic polynomials of the [Formula: see text] principal submatrices of [Formula: see text] are all equal. Such matrices are called [Formula: see text]-spectrally monomorphic. A crucial step to obtain this characterization is proving that if a matrix [Formula: see text] is [Formula: see text]-spectrally monomorphic then it is [Formula: see text]-spectrally monomorphic for [Formula: see text] in [Formula: see text].