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On the rank of random matrices

✍ Scribed by C. Cooper

Publisher
John Wiley and Sons
Year
2000
Tongue
English
Weight
209 KB
Volume
16
Category
Article
ISSN
1042-9832

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✦ Synopsis

Let M = m ij be a random n Γ— n matrix over GF(2). Each matrix entry m ij is independently and identically distributed, with Pr m ij = 0 = 1 -p n and Pr m ij = 1 = p n . The probability that the matrix M is nonsingular tends to c 2 β‰ˆ 0 28879 provided min p 1 -p β‰₯ log n + d n /n for any d n β†’ ∞. Sharp thresholds are also obtained for constant d n . This answers a question posed in a paper by

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