No abstract

In this paper, the q−radius stability of a matrix polynomial P (λ) relative to an open region Ω of the complex plane and its relation to the q−numerical range of P (λ) are investigated. Also, we obtain a lower bound that involves the distance of Ω to the connected components of the q−numerical range of P (λ).

In this paper, the [Formula: see text]-radius stability of a matrix polynomial [Formula: see text] relative to a domain [Formula: see text] of the complex plane and its relation with the [Formula: see text]-numerical range of [Formula: see text] are investigated. By using an expression of the [Formula: see text]-radius stability, we obtain a lower bound which involves the distance of [Formula: see text] from the connected components of the [Formula: see text]-numerical range of [Formula: see text].

A matrix A is called reflexive if and only if Lat(A) ⊆ Lat(B) implies that B = p(A) for some polynomial p. In this article, we characterize reflexive non-derogatory matrices.