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##### Product of diagonal entries of the unitary orbit of a 3-by-3 normal matrix

**Authors**: H Nakazato, N Bebiano , J da Providencia

**Ref.**: LINEAR ALGEBRA AND ITS APPLICATIONS **429**, 698-715 (2008)

**Abstract**: Let N be a 3 x 3 normal matrix. We investigate the sets W-k(Pi) (N) = {Pi(k)(l=1)(UNU*)ll : U epsilon U(3)} where U(3) is the group of 3 x 3 unitary matrices and I <= k <= 3. Geometric properties of these sets are studied, namely, star-shapedness and simple connectedness are investigated. A method for the numerical estimation of W-k(Pi) (N) is also provided for normal matrices of size 3