On the Kippenhahn Curves of Kronecker Products

Abstract

In many physical applications, we must solve a system of linear equations AXB=C. We know that the Kronecker product can get a convenient representation for linear equations AXB=C. In this paper, let A and C be deoted 4x4 reducible companion matrices. We study the property of the Kippenhahn curve C_R(C) and of the numerical rang W(A) being an elliptic disc by making use of matrices Kronecker product and the Kippenhahn curve C_R(C) continuely .