On determinants of random symmetric matrices over
94. R. P. Brent and
B. D. McKay,
Determinants and ranks of random matrices over
Discrete Mathematics 66 (1987), 35-49.
Also appeared as
Report CMA-R25-85, Centre for Mathematical Analysis,
ANU, August 1985, 17 pp.
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,
Go to next publication
Return to Richard Brent's index page