An n×n skew-symmetric matrix is totally positive exactly when its n(n−1)/2 selected signed minors are positive, and its Pfaffians then follow one universal sign rule.
Positively oriented matroids are realizable
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Totally positive skew-symmetric matrices
An n×n skew-symmetric matrix is totally positive exactly when its n(n−1)/2 selected signed minors are positive, and its Pfaffians then follow one universal sign rule.