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