Abstract
In this note we obtain a formula for the number of orthants intersected by a subspace of Rn. Stiemke's theorem and ipso the above mentioned transposition theorem will be obtained as a direct consequence of the formula. We employ the following terminology. The hyperplanes H1, * * *, H8 of Rn (s > n) are said to be in general position if the intersection of any n of them is 0. The k-dimensional subspace S of Rn is said to be in general position if the n subspaces HinS, where Hi= {xIxi=0} (1 0, 1 ? i ? n } where {}i I denotes any fixed choice of + l's. We now prove the following:
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