Abstract
Let $P(z):=\sum\limits^{n}_{j=0}A_jz^j$, Aj ∈ ℂm×m, 0 ≤ j ≤ n be a matrix polynomial of degree n, such that An ≥ An-1 ≥ . . . ≥ A0 ≥ 0, An > 0. Then the eigenvalues of P(z) lie in the closed unit disk. This theorem proved by Dirr and Wimmer [IEEE Trans. Automat. Control 52(2007), 2151-2153] is infact a matrix extension of a famous and elegant result on the distribution of zeros of polynomials known as Eneström-Kakeya theorem. In this paper, we prove a more general result which inter alia includes the above result as a special case. We also prove an improvement of a result due to Lê, Du, Nguyên [Oper. Matrices, 13(2019), 937-954] besides a matrix extention of a result proved by Mohammad [Amer. Math. Monthly, vol.74, No.3, March 1967].