Linear Groups of Isometries with Poset Structures
نویسندگان
چکیده
Let V be an n-dimensional vector space over a finite field Fq and P = {1, 2, . . . , n} a poset. We consider on V the poset-metric dP . In this paper, we give a complete description of groups of linear isometries of the metric space (V, dP ), for any poset-metric dP . We show that a linear isometry induces an automorphism of order in poset P , and consequently we show the existence of a pair of ordered bases of V relative to which every linear isometry is represented by an n×n upper triangular matrix.
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