Groups Preserving Ordering in Vectors
نویسنده
چکیده
where 7T is an element of the symmetric group Y'" (i.e., 7T is a permutation of 1,2, ... , n), 7=(tlt2 ... til), and E i.j is the elementary matrix with 1 in the i, j position and 0 elsewhere. In other words, P 1T(7) is the permutation matrix corresponding to 7T with the 1 in the ith row replaced by ti for each 1 = 1,2, . , " n. Our results are THEOREM 1. Let M(V) denote the group of all nonsingular matrices M such that VM = V (with a similar definitionfor M(Vo)). Then
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