## Complementary orthogonal subspaces of Rn̳ and orientability of matroids |

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### Contents

BLOCKING PAIRS ARISING FROM COMPLEMENTARY ORTHOGONAL | 33 |

Two Classes of Blocking Pairs | 37 |

ORIENTABILITY OF MATROIDS | 40 |

1 other sections not shown

### Common terms and phrases

3-painting algorithm augmenting with respect Axiom B(X+XP blocking matrix blocking pair called cocircuit matrix A(B combinatorial complementary orthogonal subspaces component coordinatizable corresponding cut in G digraphoids dissonant division ring dual pair duality theorem elementary vectors extreme solution Fano matroid Farkas lemma feasible flow feasible solution following alternatives holds Fulkerson hence holds for B,A incidence matrix ir"A ith row jth column Let 0(M linear programming problems matrix L(B max-flow min-cut theorem maximum flow problem min-min minimal s-t cuts natural orientation network flow nonnegative nonzero optimal solution orientation of M,M oriented cocircuit matrix oriented matroids packing problem pair of matrices pair of oriented pivotal operation problem 2.1 Proof proper matrix real matric matroids red edge regular matroids row space satisfies set-wise minimal s-t signed set signed support similarly oriented simplex method solution of 4.1 standard representative matrix subsets subspaces of Rn Suppose Theorem 5.1 y-orientable