Year: 2010
Type: preprint
Abstract: A $n\times n$ matrix $A$, which has a certain sign-symmetric structure ($J$--sign-symmetric), is studied in this paper. It is shown that such a matrix is similar to a nonnegative matrix. The existence of the second in modulus positive eigenvalue $λ_2$ of a $J$--sign-symmetric matrix $A$, or an odd number $k$ of simple eigenvalues, which coincide with the $k$-th roots of $ρ(A)^k$, is proved under the additional condition that its second compound matrix is also $J$--sign-symmetric. The conditions when a $J$--sign-symmetric matrix with a $J$--sign-symmetric second compound matrix has complex eigenvalues, which are equal in modulus to $ρ(A)$, are given.
Source: arXiv (Cornell University)
Author: Kushel, O. Y.
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4394635308