Maximum Likelihood Duality for Determinantal Varieties
Algebraic Geometry
2017-10-10 v3
Abstract
In a recent paper, Hauenstein, Sturmfels, and the second author discovered a conjectural bijection between critical points of the likelihood function on the complex variety of matrices of rank r and critical points on the complex variety of matrices of co-rank r-1. In this paper, we prove that conjecture for rectangular matrices and for symmetric matrices, as well as a variant for skew-symmetric matrices. To appear in International Mathematics Research Notices.
Cite
@article{arxiv.1211.3196,
title = {Maximum Likelihood Duality for Determinantal Varieties},
author = {Jan Draisma and Jose Rodriguez},
journal= {arXiv preprint arXiv:1211.3196},
year = {2017}
}