Diagonal imbeddings in a normal matrix

Abstract: Let a normal matrix and a given point in its numerical range that is not an eigenvalue. In this paper, we study the problem of construction of an isometry (), such that , where the ’s do not belong to the spectrum , for . In particular, the smallest integer k is determined, such that an isometry W exists, and our approach for W is based on the construction of mutually orthogonal and A-orthogonal vectors of . [Copyright &y& Elsevier]