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UID:www.tcs.tifr.res.in/event/1441
DTSTAMP:20240722T043611Z
SUMMARY:Equivalence Testing of Principal Minors
DESCRIPTION:Speaker: Roshan Raj (IIT Bombay)\n\nAbstract: \nFor a square ma
 trix A with n rows and n columns and a subset S of [n]\, the corresponding
  principal minor is the determinant of the submatrix of A with rows and co
 lumns indexed by elements in S i.e. det(A[S\, S]). Two operations on a mat
 rix A that preserve all the principal minors are:\nTaking the transpose of
  the matrix.\nMultiplying it by an invertible diagonal matrix on one side 
 and by its inverse on the other.\nThe matrices DAD^{-1} and DA^TD^{-1} are
  called diagonally similar to A when D is an invertible diagonal matrix.\n
 For a square matrix A of dimension n\, a subset S of [n] of size at least 
 two and at most n-2 is called a cut if the rank of both the submatrices A[
 S\, [n]-S] and A[[n]-S\, S] is less than two. In a couple of works\, Rapha
 el and Loewy showed that for an irreducible matrix A with no cuts\, anothe
 r matrix B has the same principal minors if and only if B is diagonally si
 milar to A. \nIn this work\, we give an extension of their result by givi
 ng a complete characterization of when two matrices can have the same prin
 cipal minors and give a polynomial time algorithm to test it. We also pres
 ent some applications of equivalence testing of principal minors in Combin
 atorics and Polynomial Identity Testing.\nThis is joint work with Abhranil
  Chatterjee\, Rohit Gurjar\, and  Sumanta Ghosh.\nShort Bio:\nRoshan Raj 
 is a PhD student in the CSE department at IIT Bombay working under the me
 ntorship of Prof. Rohit Gurjar. He holds a Betch degree in CSE from IIT B
 HU.\n
URL:https://www.tcs.tifr.res.in/web/events/1441
DTSTART;TZID=Asia/Kolkata:20240802T160000
DTEND;TZID=Asia/Kolkata:20240802T170000
LOCATION:via Zoom in A201
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