TY - JOUR
T1 - Perturbed identity matrices have high rank
T2 - Proof and applications
AU - Alon, Noga
PY - 2009/3
Y1 - 2009/3
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=67649235151&partnerID=8YFLogxK
U2 - 10.1017/S0963548307008917
DO - 10.1017/S0963548307008917
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:67649235151
VL - 18
SP - 3
EP - 15
JO - Combinatorics Probability and Computing
JF - Combinatorics Probability and Computing
SN - 0963-5483
IS - 1-2
ER -