Ob 'file Rank of Ilfcidelice Ma.!rlces in Finite Geometries Oiiversift' of Bom'll Calolilia on the R~ of Incidence Matrices in Finite Geometries
نویسندگان
چکیده
!he incidence matrix If of points and d-flats in PG(t, q) is a (O,l)-matrix which may be considered a _trAx with entries from the field GF (q) , where q is a prime power, q'" p. Let r d (t, 9.) denote thr rank of If over (JF (q). In this paper, & fonml.a for r t 1 (t, q) and an upper bound for r (t,q), 1 S d S t-l, are given. In the case q =p, the 'bound on rd(t,p) is attained. Similar results are given for the ruk of the incidence matrix of points and d-fiats mot passing through the origin iD J:G(t,q). Proofs of the results stated in this paper are omitted and are given in the author's Ph. D. dissertation.
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