Open AccessSome estimates of norms of random matrices
Author(s) -
Rafał Latała
Publication year - 2004
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/s0002-9939-04-07800-1
Subject(s) - algorithm , parenthesis , artificial intelligence , mathematics , computer science , philosophy , linguistics
We show that for any random matrix ( X i j ) (X_{ij}) with independent mean zero entries \[ E ‖ ( X i j ) ‖ ≤ C ( max i ∑ j E X i j 2 + max j ∑ i E X i j 2 + ∑ i j E X i j 4 4 ) , \mathbf {E}\|(X_{ij})\|\leq C \Big (\max _{i}\sqrt {\sum _{j}\mathbf {E} X_{ij}^{2}}+ \max _{j}\sqrt {\sum _{i}\mathbf {E} X_{ij}^{2}}+ \sqrt [4]{\sum _{ij} \mathbf {E} X_{ij}^{4}} \Big ), \] where C C is some universal constant.