The Hermitian Distance degree of an algebraic variety

TL;DR

This paper extends the concept of Euclidean Distance degree to Hermitian Distance degree, providing an algebraic framework for finding minimum distance points on algebraic varieties with respect to Hermitian distance.

Contribution

It introduces a generalized algebraic theory for Hermitian Distance degree, expanding the Euclidean Distance degree concept to complex Hermitian forms.

Findings

The theory generalizes Euclidean Distance degree to Hermitian settings.

Examples demonstrate the robustness and applicability of the new machinery.

Provides algebraic tools for minimum Hermitian distance problems.

Abstract

In this paper we develop an algebraic theory to study the problem of finding the minimum distance point from an algebraic variety with respect to the Hermitian distance function. The theory generalizes the Euclidean Distance degree introduced in arXiv:1309.0049, replacing a positive symmetric bilinear form by a Hermitian form. Various examples are presented to show the robustness of the machineries.