Characterization of -spectrally monomorphic Hermitian matrices
K Attas, A Boussaïri, I Souktani - arXiv preprint arXiv:1907.05817, 2019 - arxiv.org
K Attas, A Boussaïri, I Souktani
arXiv preprint arXiv:1907.05817, 2019•arxiv.orgThis paper solves the following problem about Hermitian matrices related to the theory of $2
$-structures:\emph {} Let $ n $ be a positive integer and $ k $ be an integer with $
k\in\{3,\ldots, n-3\} $. Characterize the Hermitian matrices $ A $ such that the characteristic
polynomials of the $ k\times 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 …
$-structures:\emph {} Let $ n $ be a positive integer and $ k $ be an integer with $
k\in\{3,\ldots, n-3\} $. Characterize the Hermitian matrices $ A $ such that the characteristic
polynomials of the $ k\times 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 …
This paper solves the following problem about Hermitian matrices related to the theory of -structures:\emph{ }Let be a positive integer and be an integer with . Characterize the Hermitian matrices such that the characteristic polynomials of the submatrices of are all equal. Such matrices are called -spectrally monomorphic. A crucial step to obtain this characterization is proving that if a matrix is -spectrally monomorphic then it is -spectrally monomorphic for in .
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