Characterization of k-spectrally monomorphic Hermitian matrices

2019/07/12 by Attas, Kawtar, Boussaïri, Abderrahim, Souktani, Imane
#05C50 #15B57 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1907.05817

Abstract

This paper solves the following problem about Hermitian matrices related to the theory of 2-structures: Let n be a positive integer and k be an integer with k∈ \3,…,n-3\. Characterize the Hermitian matrices A such that the characteristic polynomials of the k× k submatrices of A are all equal. Such matrices are called k-spectrally monomorphic. A crucial step to obtain this characterization is proving that if a matrix A is k-spectrally monomorphic then it is l-spectrally monomorphic for l in \1,…,min\k, n-k\\.

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