TR24-150 Authors: Abhranil Chatterjee, Sumanta Ghosh, Rohit Gurjar, Roshan Raj

Publication: 5th October 2024 14:14

Downloads: 86

Keywords:

Two matrices are said to be principal minor equivalent if they have equal

corresponding principal minors of all orders. We give a characterization of

principal minor equivalence and a deterministic polynomial time algorithm to

check if two given matrices are principal minor equivalent. Earlier such

results were known for certain special cases like symmetric matrices,

skew-symmetric matrices with {0, 1, -1}-entries, and matrices with no cuts

(i.e., for any non-trivial partition of the indices, the top right block or the

bottom left block must have rank more than 1).

As an immediate application, we get an algorithm to check if the

determinantal point processes corresponding to two given kernel matrices (not

necessarily symmetric) are the same. As another application, we give a

deterministic polynomial-time test to check equality of two multivariate

polynomials, each computed by a symbolic determinant with a rank 1 constraint

on coefficient matrices.