BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Mark Rudelson (University of Michigan) DTSTART:20230118T140000Z DTEND:20230118T150000Z DTSTAMP:20260423T035533Z UID:ADPS/10 DESCRIPTION:Title: Ap proximately Hadamard matrices and random frames\nby Mark Rudelson (Uni versity of Michigan) as part of Abu Dhabi Stochastics Seminar\n\n\nAbstrac t\nAn n by n matrix with plus-minus 1 entries which acts as a scaled isome try is called Hadamard. Such matrices exist in some\, but not all dimensio ns. Combining number-theoretic and probabilistic tools we construct matric es with plus-minus 1 entries which act as approximate scaled isometries fo r all 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 vec tors which allows a robust decomposition of any vector in the space as a l inear combination of these vectors. Frames are used in signal processing s ince the loss of a fraction of coordinates does not prevent the recovery o f the signal. We will discuss a question when a random frame contains a co py of a nice basis. Joint work with Xiaoyu Dong.\n LOCATION:https://researchseminars.org/talk/ADPS/10/ END:VEVENT END:VCALENDAR