Grassmann and Flag Varieties in Linear Algebra, Optimization, and Statistics: An Algebraic Perspective
Hannah Friedman, Serkan Hoşten
公開日: 2025/5/21
Abstract
Grassmann and flag varieties lead many lives in pure and applied mathematics. Here we focus on the algebraic complexity of solving various problems in linear algebra and statistics as optimization problems over these varieties. The measure of the algebraic complexity is the amount of complex critical points of the corresponding optimization problem. After an exposition of different realizations of these manifolds as algebraic varieties we present a sample of optimization problems over them and we compute their algebraic complexity.