Perturbed identity matrices have high rank: Proof and applications

Noga Alon*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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


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