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UID:www.tcs.tifr.res.in/event/1162
DTSTAMP:20230914T125953Z
SUMMARY:Commuting Matrices and Multivariate Multiplicity
DESCRIPTION:Speaker: Anamay Tengse\n\nAbstract: \nWe know that for matrices
  A and B\, AB is not the same as BA in general. But suppose B is a polynom
 ial in A\, like B = A^2 - 3A + I (note I = A^0). Then AB is indeed the sam
 e as BA. Some natural questions follow for a set S of (square) matrices th
 at commute with each other.\n1. Does there always exist an A in S that "ge
 nerates" the rest via polynomials?\n2. Since diagonal matrices commute wit
 h each other\, is it the case that we can (simultaneously) diagonalise all
  matrices in S?\n3. If (1) and (2) are false\, then what do these non-triv
 ial sets S look like?\nIn this talk we will see an elegant characterisatio
 n of commuting matrices which follows from the works of Marinari\, Möller
  and Mora (1993)\, and Möller and Stetter (1995). Similar in spirit to qu
 estion (1) above\, the characterisation involves multivariate polynomials 
 and uses a notion of "multiplicity of a polynomial at a point" that is sli
 ghtly non-standard in CS.\n\nZoom link:\nhttps://zoom.us/j/93889521556?pwd
 =eEFJWVRtRHNpNlpZWmhNYTJGQTF6Zz09\n \n
URL:https://www.tcs.tifr.res.in/web/events/1162
DTSTART;TZID=Asia/Kolkata:20210917T171500
DTEND;TZID=Asia/Kolkata:20210917T181500
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