Perturbed identity matrices have high rank: Proof and applications
N Alon - Combinatorics, Probability and Computing, 2009 - cambridge.org
Combinatorics, Probability and Computing, 2009•cambridge.org
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.
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.
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.
Cambridge University Press