1Department of Mathematics, Shahid Bahonar University of Kerman, 76169-14111, Kerman, Iran.
2Department of Mathematics, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran.
In this paper, the notion of rankk numerical range of rectangular complex ma-
trix polynomials are introduced. Some algebraic and geometrical properties are investigated.
Moreover, for ϵ > 0; the notion of Birkho-James approximate orthogonality sets for ϵhigher
rank numerical ranges of rectangular matrix polynomials is also introduced and studied. The
proposed denitions yield a natural generalization of the standard higher rank numerical