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Perturbed Identity Matrices Have High Rank: Proof and Applications

Published online by Cambridge University Press:  01 March 2009

NOGA ALON
NOGA ALON*
Affiliation:
Schools of Mathematics and Computer Science, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel (e-mail: nogaa@tau.ac.il)
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Abstract

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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.

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