Kippenhahn Varieties and the Weyl Calculus for Several Matrices I

TL;DR

This paper explores the relationship between Kippenhahn varieties and the Weyl functional calculus for multiple matrices, revealing how algebraic geometry informs the support of the calculus for hermitian matrices.

Contribution

It establishes a connection between Kippenhahn varieties and the support of the Weyl calculus for several hermitian matrices, advancing the understanding of their algebraic geometric properties.

Findings

Support and singular support are characterized by Kippenhahn varieties.

The paper links the Weyl calculus to the generalized numerical range.

Provides geometric insights into the functional calculus for matrices.

Abstract

The paper reviews properties of the Weyl functional calculus for several operators and its relation to the generalised numerical range of $n$ hermitian matrices. The support and singular support of the Weyl functional calculus for $n$ hermitian matrices are determined by Kippenhahn varieties in algebraic geometry.