Notice of RetractionOn the Kippenhahn Curves of Fan Product

Notice of Retraction

After careful and considered review of the content of this paper by a duly constituted expert committee, this paper has been found to be in violation of IEEE´s Publication Principles.

We hereby retract the content of this paper. Reasonable effort should be made to remove all past references to this paper.

The presenting author of this paper has the option to appeal this decision by contacting TPII@ieee.org.

The research of Kronecker sum, Kronecker product, and fan product of matrix has actual meaning and the theories meaning since a lot of problems can convert into the related calculation problems of the matrices fan product at the signal, picture processing and mathematics etc. On account of the wide application of Kronecker sum, Kronecker product and fan product in the solving process of sparse linear algebra equations, in this paper, let A and C be denoted 4 ?? 4 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 sum, Kronecker product and fan product and the Kippenhahn curve C_R(C) continually.