ON LOW-DIMENSIONAL PARTIAL ISOMETRIES

Qixiao He; Ilya M. Spitkovsky; Ibrahim Suleiman

doi:10.13001/ela.2023.7405

ON LOW-DIMENSIONAL PARTIAL ISOMETRIES

Qixiao He, Ilya M. Spitkovsky, Ibrahim Suleiman

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Two statements concerning n-by-n partial isometries are being considered: (i) these matrices are generic, if unitarily irreducible, and (ii) if nilpotent, their numerical ranges are circular disks. Both statements hold for n ≤ 4 but fail starting with n = 5.

Original language	English (US)
Pages (from-to)	124-135
Number of pages	12
Journal	Electronic Journal of Linear Algebra
Volume	39
DOIs	https://doi.org/10.13001/ela.2023.7405
State	Published - 2023

Keywords

Kippenhahn polynomial
Numerical range
Partial isometry

ASJC Scopus subject areas

Algebra and Number Theory

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10.13001/ela.2023.7405

Cite this

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title = "ON LOW-DIMENSIONAL PARTIAL ISOMETRIES",

abstract = "Two statements concerning n-by-n partial isometries are being considered: (i) these matrices are generic, if unitarily irreducible, and (ii) if nilpotent, their numerical ranges are circular disks. Both statements hold for n ≤ 4 but fail starting with n = 5.",

keywords = "Kippenhahn polynomial, Numerical range, Partial isometry",

author = "Qixiao He and Spitkovsky, {Ilya M.} and Ibrahim Suleiman",

year = "2023",

doi = "10.13001/ela.2023.7405",

language = "English (US)",

volume = "39",

pages = "124--135",

journal = "Electronic Journal of Linear Algebra",

issn = "1537-9582",

publisher = "International Linear Algebra Society",

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T1 - ON LOW-DIMENSIONAL PARTIAL ISOMETRIES

AU - He, Qixiao

AU - Spitkovsky, Ilya M.

AU - Suleiman, Ibrahim

PY - 2023

Y1 - 2023

N2 - Two statements concerning n-by-n partial isometries are being considered: (i) these matrices are generic, if unitarily irreducible, and (ii) if nilpotent, their numerical ranges are circular disks. Both statements hold for n ≤ 4 but fail starting with n = 5.

AB - Two statements concerning n-by-n partial isometries are being considered: (i) these matrices are generic, if unitarily irreducible, and (ii) if nilpotent, their numerical ranges are circular disks. Both statements hold for n ≤ 4 but fail starting with n = 5.

KW - Kippenhahn polynomial

KW - Numerical range

KW - Partial isometry

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U2 - 10.13001/ela.2023.7405

DO - 10.13001/ela.2023.7405

M3 - Article

AN - SCOPUS:85158988157

SN - 1537-9582

VL - 39

SP - 124

EP - 135

JO - Electronic Journal of Linear Algebra

JF - Electronic Journal of Linear Algebra

ER -

ON LOW-DIMENSIONAL PARTIAL ISOMETRIES

Abstract

Keywords

ASJC Scopus subject areas

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