Perturbed identity matrices have high rank: Proof and applications

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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.

Original languageEnglish (US)
Pages (from-to)3-15
Number of pages13
JournalCombinatorics Probability and Computing
Issue number1-2
StatePublished - Mar 2009
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Statistics and Probability
  • Computational Theory and Mathematics
  • Applied Mathematics


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