On Kippenhahn curves of low rank partial isometries
Nikita Popov, Eric Shen, Ilya M. Spitkovsky
TL;DR
This paper investigates the geometric properties of Kippenhahn curves for low-rank partial isometries, characterizing when these curves contain circular components and confirming a conjecture for these matrices.
Contribution
It provides conditions for rank three partial isometries to have circular components in their Kippenhahn curves and verifies the Gau-Wang-Wu conjecture for these matrices.
Findings
Rank three partial isometries can have circular components in their Kippenhahn curves.
Matrices with circular numerical ranges are characterized.
The Gau-Wang-Wu conjecture holds for the considered matrices.
Abstract
Conditions are established for rank three partial isometries to have circular components contained in their Kippenhahn curves. In particular, such matrices with circular numerical ranges are described. It is also established that the Gau-Wang-Wu conjecture holds for matrices under consideration.
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Taxonomy
TopicsMatrix Theory and Algorithms · Mathematical Inequalities and Applications · Holomorphic and Operator Theory