TL;DR
This paper determines the minimal defining equations of the Kalman variety, a space of endomorphisms with an eigenvector in a given subspace, resolving a conjecture and advancing understanding in algebraic geometry.
Contribution
It provides the first complete description of the minimal equations defining the Kalman variety over characteristic zero fields.
Findings
Resolved a conjecture of Ottaviani and Sturmfels.
Derived the minimal defining equations of the Kalman variety.
Advances algebraic understanding of eigenvector-related varieties.
Abstract
The Kalman variety of a linear subspace is a vector space consisting of all endomorphisms that have an eigenvector in that subspace. We resolve a conjecture of Ottaviani and Sturmfels and give the minimal defining equations of the Kalman variety over a field of characteristic 0.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Aerospace Engineering and Control Systems · Control and Dynamics of Mobile Robots