✦ LIBER ✦

Determinants and ranks of random matrices over Zm

✍ Scribed by Richard P Brent; Brendan D McKay

Publisher: Elsevier Science
Year: 1987
Tongue: English
Weight: 739 KB
Volume: 66
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(87)90117-8

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✦ Synopsis

Let Zm be the ring of integers modulo m. The m-rank of an integer matrix is the largest order of a square submatrix whose determinant is not divisible by m. We determine the probability that a random rectangular matrix over ~Ym has a specified m-rank and, if it is square, a specified determinant. These results were previously known only for prime m.

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