Diagonal imbeddings in a normal matrix

Let a normal matrix A∈Cn×nA∈Cn×n and μ1μ1 a given point in its numerical range w(A)w(A) that is not an eigenvalue. In this paper, we study the problem of construction of an isometry W∈Cn×(n-k)W∈Cn×(n-k) (1⩽k