Fix q and let Mn be an n x n matrix with entries drawn independently from the finite field Fq according to some distribution μn. It is shown that, except in certain pathological cases, the probability that Mn is nonsingular is asymptotically the same as for uniform entries; that is, Pr(Mn is nonsingular) Πi≥1 (1 - q-i) as n → ∞.
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Statistics and Probability
- Computational Theory and Mathematics
- Applied Mathematics