Correction to "On the existence and uniqueness of the eigenvalue decomposition of a parahermitian matrix"

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Abstract

In Weiss (2018), we stated that any positive semi-definite parahermitian matrix R(z): C→CMxM that is analytic on an annulus containing at least the unit circle will admit a decomposition with analytic eigenvalues and analytic eigenvectors. In this note, we further qualify this statement, and define the class of matrices that fulfills the above properties yet does not admit an analytic EVD. We follow the
notation in Weiss (2018).
LanguageEnglish
Pages6325-6327
Number of pages3
JournalIEEE Transactions on Signal Processing
Volume66
Issue number23
Early online date1 Nov 2018
DOIs
Publication statusPublished - 1 Dec 2018

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Decomposition
Eigenvalues and eigenfunctions

Keywords

  • hermitian matrix
  • parahermitian matrix
  • eigenvalue decomposition algorithm

Cite this

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title = "Correction to {"}On the existence and uniqueness of the eigenvalue decomposition of a parahermitian matrix{"}",
abstract = "In Weiss (2018), we stated that any positive semi-definite parahermitian matrix R(z): C→CMxM that is analytic on an annulus containing at least the unit circle will admit a decomposition with analytic eigenvalues and analytic eigenvectors. In this note, we further qualify this statement, and define the class of matrices that fulfills the above properties yet does not admit an analytic EVD. We follow thenotation in Weiss (2018).",
keywords = "hermitian matrix, parahermitian matrix, eigenvalue decomposition algorithm",
author = "Stephan Weiss and Jennifer Pestana and Proudler, {Ian K.} and Coutts, {Fraser K.}",
year = "2018",
month = "12",
day = "1",
doi = "10.1109/TSP.2018.2877142",
language = "English",
volume = "66",
pages = "6325--6327",
journal = "IEEE Transactions on Signal Processing",
issn = "1053-587X",
number = "23",

}

TY - JOUR

T1 - Correction to "On the existence and uniqueness of the eigenvalue decomposition of a parahermitian matrix"

AU - Weiss, Stephan

AU - Pestana, Jennifer

AU - Proudler, Ian K.

AU - Coutts, Fraser K.

PY - 2018/12/1

Y1 - 2018/12/1

N2 - In Weiss (2018), we stated that any positive semi-definite parahermitian matrix R(z): C→CMxM that is analytic on an annulus containing at least the unit circle will admit a decomposition with analytic eigenvalues and analytic eigenvectors. In this note, we further qualify this statement, and define the class of matrices that fulfills the above properties yet does not admit an analytic EVD. We follow thenotation in Weiss (2018).

AB - In Weiss (2018), we stated that any positive semi-definite parahermitian matrix R(z): C→CMxM that is analytic on an annulus containing at least the unit circle will admit a decomposition with analytic eigenvalues and analytic eigenvectors. In this note, we further qualify this statement, and define the class of matrices that fulfills the above properties yet does not admit an analytic EVD. We follow thenotation in Weiss (2018).

KW - hermitian matrix

KW - parahermitian matrix

KW - eigenvalue decomposition algorithm

UR - https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78

UR - https://doi.org/10.1109/TSP.2018.2812747

UR - https://strathprints.strath.ac.uk/63359/

U2 - 10.1109/TSP.2018.2877142

DO - 10.1109/TSP.2018.2877142

M3 - Article

VL - 66

SP - 6325

EP - 6327

JO - IEEE Transactions on Signal Processing

T2 - IEEE Transactions on Signal Processing

JF - IEEE Transactions on Signal Processing

SN - 1053-587X

IS - 23

ER -