|Responsables :||E. Abakoumov - A.Eskenazis - D. Cordero-Erausquin - M. Fathi - O. Guédon - B. Maurey|
|Email des responsables :|
|Salle :||salle 13 - couloir 15-16 - 4ème étage|
|Adresse :||Campus Pierre et Marie Curie|
Le Jeudi à 10h30 - IMJ-PRG - 4 place Jussieu - 75005 PARIS
|Orateur(s)||Mark Rudelson - University of Michigan,|
|Titre||Approximately Hadamard matrices and random frames|
|Horaire||10:30 à 12:00|
An n by n matrix with plus-minus 1 entries which acts as a scaled isometry is called Hadamard. Such matrices exist in some, but not all dimensions. Combining number-theoretic and probabilistic tools we construct matrices with plus-minus 1 entries which act as scaled approximate isometries for any n. More precisely, the matrices we construct have condition numbers bounded by a constant independent of the dimension.
We will also discuss an application in signal processing. A frame is an overcomplete set of vectors which allows a robust decomposition of any vector in the space as a linear combination of these vectors. Frames are used in signal processing since the loss of a fraction of coordinates does not prevent the recovery of the signal. We will discuss a question when a random frame contains a copy of a nice basis.
|Salle||salle 13 - couloir 15-16 - 4ème étage|
|Adresse||Campus Pierre et Marie Curie|