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An n × n complex matrix is full ray-nonsingular if it has no zero entries and every matrix obtained by changing the magnitudes of its entries is nonsingular. It is shown that a 5 × 5f ull ray-nonsingular matrix does not exist. This, combined with earlier results, shows that there exists an n × n full ray-nonsingular matrix if and only if n ≤ 4.

Non-existence of 5X5 full ray nonsingular matrices