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Isospectrality and matrices with concentric circular higher rank numerical ranges
Journal article   Open access   Peer reviewed

Isospectrality and matrices with concentric circular higher rank numerical ranges

Edward Poon and Hugo J. Woerdeman
Linear algebra and its applications, v 631, pp 174-180
15 Dec 2021
url
https://doi.org/10.1016/j.laa.2021.08.025View
Accepted (AM)Maybe Open Access (Publisher Bronze) Open

Abstract

Higher rank numerical range Isospectral Lax pair Trigonometric pencil
We characterize under what conditions n×n Hermitian matrices A1 and A2 have the property that the spectrum of cos⁡tA1+sin⁡tA2 is independent of t (thus, the trigonometric pencil cos⁡tA1+sin⁡tA2 is isospectral). One of the characterizations requires the first ⌈n2⌉ higher rank numerical ranges of the matrix A1+iA2 to be circular disks with center 0. Finding the unitary similarity between cos⁡tA1+sin⁡tA2 and, say, A1 involves finding a solution to Lax's equation.

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Collaboration types
Domestic collaboration
Web of Science research areas
Mathematics
Mathematics, Applied
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