Abstract

Every partial TP2 (TP1) matrix with one unspecified entry has a TP2 (TP1) com- pletion. For a given m-by-n pattern with one unspecified entry, the minimum set of conditions characterizing TP3 completability is given. These conditions are at most eight polynomial inequali- ties on the specified entries of the pattern. For k � 3, patterns with one unspecified entry that are TPk completable are also characterized, and conditions are described for completability otherwise.

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