Perturbed Identity Matrices Have High Rank: Proof and Applications

  title={Perturbed Identity Matrices Have High Rank: Proof and Applications},
  author={Noga Alon},
  journal={Combinatorics, Probability & Computing},
We describe a lower bound for the rank of any real matrix in which all diagonal entries are significantly larger in absolute value than all other entries, and discuss several applications of this result to the study of problems in Geometry, Coding Theory, Extremal Finite Set Theory and Probability. This is partly a survey, containing a unified approach for proving various known results, but it contains several new results as well. 
Highly Cited
This paper has 72 citations. REVIEW CITATIONS

From This Paper

Topics from this paper.
46 Citations
20 References
Similar Papers


Publications referenced by this paper.
Showing 1-10 of 20 references

On (ε

  • N. Alon, T. Itoh, T. Nagatani
  • k)-min-wise independent permutations, Random…
  • 2007
1 Excerpt

On finite pseudorandom binary sequences , VII , The measures of pseudorandomness

  • C. Mauduit Cassaigne, A. Sárközy
  • Acta Arith .
  • 2002

A Polynomial Lower Bound for the Size of any k-Min-Wise Independent Set of Permutation

  • S. Norin
  • Zapiski Nauchnyh Seminarov
  • 2001
1 Excerpt

Similar Papers

Loading similar papers…