The inverse eigenvalue problem and the associated optimal approximation problem for Hermitian reflexive matrices with respect to a normal {k +1}-potent matrix are considered. First, we study the existence of the solutions of the associated inverse eigenvalue problem and present an explicit form for them. Then, when such a solution exists, an expression for the solution to the corresponding optimal approximation problem is obtained.
A complex square matrix A is called J-hamiltonian if AJ is hermitian where J is a normal real matrix such that J 2 = −I n . In this paper we solve the problem of finding J-hamiltonian normal solutions for the inverse eigenvalue problem.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.