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On the rank of certain matrices

โœ Scribed by Pietro Corvaja; Umberto Zannier

Publisher
John Wiley and Sons
Year
2011
Tongue
English
Weight
98 KB
Volume
284
Category
Article
ISSN
0025-584X

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โœฆ Synopsis

Osculating spaces and diophantine equations (with an Appendix by Pietro Corvaja and Umberto Zannier)" by M. Bolognesi and G. Pirola.

๐Ÿ“œ SIMILAR VOLUMES

On the Rank of Certain Incidence Matrice
On the Rank of Certain Incidence Matrices over GF(2)
โœ Phillip McClurg ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 109 KB

Let V be a vector space of dimension n โ‰ฅ 3 over GF(2). We are concerned with the incidence of k-dimensional subspaces in (k + 2)-dimensional subspaces where 1 โ‰ค k โ‰ค n -2. We compute here an upper bound for the rank of the associated incidence matrices over GF(2).

On the rank of random matrices
On the rank of random matrices
โœ C. Cooper ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 209 KB ๐Ÿ‘ 2 views

Let M = m ij be a random n ร— 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 โ‰ˆ 0 28879 provided min p 1 -p โ‰ฅ log n + d n /n for any d n โ†’ โˆž. Sharp