Research Communication | Open Access
Volume 2019 | Communication ID 60
Volume 2019 | Communication ID 60
| On k-spectrally monomorphic Hermitian matrices. |
Imane Souktani, Abderrahim Boussairi
Received |
Accepted |
Published |
Jan 15, 2019 |
Feb 26, 2019 |
Mar 01, 2019 |
Abstract: Let H be an n by n Hermitian matrix and let X , Y be two nonempty subsets of n (where n ={1,2,...,n}). We denote by H[X] the principal submatrix of H, having row and column indices in X. We say that H is k-monomorphic if all its principal submatrices of order k are isomorphic. In other words, for any subsets X and Y such that |X|=|Y|=k, H[X] and H[Y] are similar by a permutation matrix P. A Hermitian matrix is k-spectrally monomorphic if all its principal submatrices of order k have the same characteristic polynomials. A k-monomorphic Hermitian matrix is k-spectrally monomorphic. In this ...