Number of Quadratic Forms of Given Rank Sample Clauses

Number of Quadratic Forms of Given Rank. ‌ ≥ In this section we compute the number N (k, r) of rank r quadratic forms on any F-vector space of dimension k, where k, r are non-negative integers with k r. First we deal with the case k = r, i.e. of full-rank quadratic forms, then we address the general case. In the full-rank case we write N (k) instead of N (x, x), as a shorthand. We now state the results: Theorem 2.4.24 for the first case, Theorem 2.4.25 for the latter.
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