## On determinants of random symmetric matrices over
*Z*_{m}

94. R. P. Brent and
B. D. McKay,
Determinants and ranks of random matrices over
*Z*_{m} ,
* 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).

## Abstract

Let *Z*_{m} 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
*Z*_{m} has a specified
*m*-rank and, if it is square,
a specified determinant. These results were previously known only
for prime *m*.
## Comments

For related work on random symmetric matrices,
see [101].
Go to next publication

Return to Richard Brent's index page