TY - JOUR AU - Darawan Zrar Mohammed, AU - Ahmed Muhammad, PY - 2023/02/20 Y2 - 2024/03/28 TI - Generalization of numerical range of polynomial operator matrices JF - Tikrit Journal of Pure Science JA - Tikrit J. Pure Sci. VL - 28 IS - 1 SE - Articles DO - 10.25130/tjps.v28i1.1268 UR - https://tjps.tu.edu.iq/index.php/tjps/article/view/1268 SP - 75-81 AB - <p>Suppose that &nbsp;is a polynomial matrix operator where &nbsp;for , are &nbsp;complex matrix and let &nbsp;be a complex variable. For an &nbsp;Hermitian matrix , we define the -numerical range of polynomial matrix of &nbsp;as , where . In this paper we study&nbsp; &nbsp;and our emphasis is on the geometrical properties of . We consider the location of&nbsp; &nbsp;in the complex plane and&nbsp; a theorem concerning&nbsp; the boundary of is also obtained.&nbsp; Possible generalazations of our results including their extensions to bounded linerar operators on an infinite dimensional Hilbert space are described.</p> ER -