𝔖 Bobbio Scriptorium
✦   LIBER   ✦

A note on monotone complexity and the rank of matrices

✍ Scribed by Anna Gál; Pavel Pudlák


Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
96 KB
Volume
87
Category
Article
ISSN
0020-0190

No coin nor oath required. For personal study only.


📜 SIMILAR VOLUMES


A note on universally optimal matrices a
✍ Liang-Hao Huang; Gerard J. Chang; Hong-Gwa Yeh 📂 Article 📅 2010 🏛 Elsevier Science 🌐 English ⚖ 164 KB

For a simple graph G on n vertices, the minimum rank of G over a field F, written as mr F (G), is defined to be the smallest possible rank among all n × n symmetric matrices over F whose (i, j)th entry (for i / = j) is nonzero whenever {i, j} is an edge in G and is zero otherwise. A symmetric integ

On the rank of random matrices
✍ C. Cooper 📂 Article 📅 2000 🏛 John Wiley and Sons 🌐 English ⚖ 209 KB 👁 2 views

Let M = m ij be a random n × 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 ≈ 0 28879 provided min p 1 -p ≥ log n + d n /n for any d n → ∞. Sharp

On the rank of certain matrices
✍ Pietro Corvaja; Umberto Zannier 📂 Article 📅 2011 🏛 John Wiley and Sons 🌐 English ⚖ 98 KB

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