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The Convex Algebraic Geometry of Hig...

Nino-Cortes, Jonathan Andres,

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The Convex Algebraic Geometry of Higher-Rank Numerical Ranges /

Record Type:	Electronic resources : Monograph/item
Title/Author:	The Convex Algebraic Geometry of Higher-Rank Numerical Ranges // Jonathan Andres Nino-Cortes.
Author:	Nino-Cortes, Jonathan Andres,
Description:	1 electronic resource (99 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 87-01, Section: B.
Contained By:	Dissertations Abstracts International87-01B.
Subject:	Mathematics. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=32114612
ISBN:	9798288821905

The Convex Algebraic Geometry of Higher-Rank Numerical Ranges /
Nino-Cortes, Jonathan Andres,

The Convex Algebraic Geometry of Higher-Rank Numerical Ranges /Jonathan Andres Nino-Cortes. - 1 electronic resource (99 pages)

Source: Dissertations Abstracts International, Volume: 87-01, Section: B.

The higher-rank numerical range is a convex compact set generalizing the classical numerical range of a square complex matrix, first appearing in the study of quantum error correction. In this thesis, we will discuss some of the real algebraic and convex geometry of these sets, including a generalization of Kippenhahn's theorem, and describe an algorithm to explicitly calculate the higher-rank numerical range of a given matrix. We will also discuss the inverse field of values problem, an inverse problem on the numerical range. We focus on the geometric properties of the set of solutions. Finally, we consider an analogous problem for higher-rank numerical ranges and show how to solve it using the ideas behind the proof of convexity for these sets.

English

ISBN: 9798288821905Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Higher-rank numerical ranges

The Convex Algebraic Geometry of Higher-Rank Numerical Ranges /
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100 1 $a Nino-Cortes, Jonathan Andres, $e author. $3 3823217
245 1 0 $a The Convex Algebraic Geometry of Higher-Rank Numerical Ranges / $c Jonathan Andres Nino-Cortes.
264 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2025
300 $a 1 electronic resource (99 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Dissertations Abstracts International, Volume: 87-01, Section: B.
500 $a Advisors: Vinzant, Cynthia Committee members: Thomas, Rekha R.; Alper, Jarod.
502 $b Ph.D. $c University of Washington $d 2025.
520 $a The higher-rank numerical range is a convex compact set generalizing the classical numerical range of a square complex matrix, first appearing in the study of quantum error correction. In this thesis, we will discuss some of the real algebraic and convex geometry of these sets, including a generalization of Kippenhahn's theorem, and describe an algorithm to explicitly calculate the higher-rank numerical range of a given matrix. We will also discuss the inverse field of values problem, an inverse problem on the numerical range. We focus on the geometric properties of the set of solutions. Finally, we consider an analogous problem for higher-rank numerical ranges and show how to solve it using the ideas behind the proof of convexity for these sets.
546 $a English
590 $a School code: 0250
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
650 4 $a Applied mathematics. $3 2122814
653 $a Higher-rank numerical ranges
653 $a Kippenhahn's theorem
653 $a Real algebraic geometry
653 $a Symbolic computation
690 $a 0405
690 $a 0642
690 $a 0364
710 2 $a University of Washington. $b Mathematics. $e degree granting institution. $3 3823218
720 1 $a Vinzant, Cynthia $e degree supervisor.
773 0 $t Dissertations Abstracts International $g 87-01B.
790 $a 0250
791 $a Ph.D.
792 $a 2025
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=32114612