On determinants of random symmetric matrices over Zm

94. R. P. Brent and B. D. McKay, Determinants and ranks of random matrices over Zm , Discrete Mathematics 66 (1987), 35-49. MR 88h:15042.

Also appeared as Report CMA-R25-85, Centre for Mathematical Analysis, ANU, August 1985, 17 pp.

Abstract: dvi (2K), pdf (71K), ps (25K).

Paper: pdf (1218K).


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 Zm has a specified m-rank and, if it is square, a specified determinant. These results were previously known only for prime m.


For related work on random symmetric matrices, see [101].

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