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An  n  ×  n  matrix is called an  N   0 -matrix if all its specified principal minors are nonpositive. In the context of partial matrices, a partial matrix is called a partial  N   0 -matrix if all its specified principal minors are nonpositive. In this paper we characterize the existence of an  N   0 -matrix completion of a partial  N   0 -matrix whose associated graph is a directed cycle.

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Characterization of the Existence of an<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow></mml:math>-Completion of a Partial<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow></mml:math>-Matrix with an Associated Directed Cycle

Characterization of the Existence of anN0-Completion of a PartialN0-Matrix with an Associated Directed Cycle