The Property of Kippenhahn Curves of Hadamard products and Applications

摘要

In this paper, A and C will denote 4×4 reducible companion matrices, we combine the Kronecker product, Hadamard product with numerical rang of matrices, discuss the relations between the Kronecker product, Hadamard product with numerical rang of matrices, and illustrate that the kippenhahn curve C_R(C) consists of C_R(A) consists of one ellipse whose foci are λ_1=λ_3=-(a~2/(a{top}-)~2)i, λ_2=λ_4=a~2i/(a{top}-)~2 and axis has a length r.