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Topic: distribution of ranks of square matrices over F_2
Replies: 7   Last Post: Sep 4, 1997 10:53 AM

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George Marsaglia

Posts: 363
Registered: 12/7/04
Re: distribution of ranks of square matrices over F_2
Posted: Sep 3, 1997 7:22 PM
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A random n x m matrix with independent elements equally probable 0,1
has rank r=1,2,...,min(m,n) with probability

2^{r(n+m-r)-mn}\prod_{i=0}^{r-1}[(1-2^{i-n})(1-2^{i-m})/(1-2^{i-r})].

George Marsaglia

(This is the basis of one of the tests in
The Marsaglia Random Number CDROM
with
The DIEHARD Battery of Tests of Randomness

available at http://www.cs.hku.hk)









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