Non-existence of 5X5 full ray nonsingular matrices

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Chi-Kwong Li
Thomas Milligan
Bryan L. Shader


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

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