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A study for maximizing an index of an array of nonparallel wire antennas under the simultaneous determination of the polarization is carried out. The eigenvalue method is used, and it is shown that the maximum obtainable index of an antenna which has not a predefined polarization is the largest of the only two nonzero eigenvalues of the regular pencil of its matrices. The maximization is applied for cases where there are no constraints and also in cases where constraints in the pattern nulls or/and sidelobe levels are posed. Some examples are presented.