Zahra Boor Boor Azimi - Department of Mathematics, Kerman Branch, Islamic Azad University, Kerman, Iran.
Gholamreza Aghamollaei - Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.

In this paper, the notions of pseudofield of values and joint pseudofield of values of matrix polynomials are introduced and some of their algebraic and geometrical properties are studied.  Moreover, the relationship between the pseudofield of values of a matrix polynomial and the pseudofield of values of its companion linearization is stated, and then some properties of the augmented field of values of basic A-factor block circulant matrices are investigated.

‎Field of values, Perturbation, Matrix polynomial, companion linearization, Basic $A-$factor block circulant matrix