The minimization of matrix logarithms: On a fundamental property of the unitary polar factor

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Autoren

  • Johannes Lankeit
  • Patrizio Neff
  • Yuji Nakatsukasa

Externe Organisationen

  • Universität Duisburg-Essen
  • University of Tokyo (UTokyo)
Forschungs-netzwerk anzeigen

Details

OriginalspracheEnglisch
Seiten (von - bis)28-42
Seitenumfang15
FachzeitschriftLinear Algebra and Its Applications
Jahrgang449
Frühes Online-Datum26 Feb. 2014
PublikationsstatusVeröffentlicht - 15 Mai 2014
Extern publiziertJa

Abstract

We show that the unitary factor Up in the polar decomposition of a nonsingular matrix Z=UpH is a minimizer for both∥-Log(Q *Z)∥-and∥-sym*(Log(Q *Z))∥- over the unitary matrices QεU(n) for any given invertible matrix ZεCn n×, for any unitarily invariant norm and any n. We prove that Up is the unique matrix with this property to minimize all these norms simultaneously. As important tools we use a generalized Bernstein trace inequality and the theory of majorization.

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The minimization of matrix logarithms: On a fundamental property of the unitary polar factor. / Lankeit, Johannes; Neff, Patrizio; Nakatsukasa, Yuji.
in: Linear Algebra and Its Applications, Jahrgang 449, 15.05.2014, S. 28-42.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Lankeit J, Neff P, Nakatsukasa Y. The minimization of matrix logarithms: On a fundamental property of the unitary polar factor. Linear Algebra and Its Applications. 2014 Mai 15;449:28-42. Epub 2014 Feb 26. doi: 10.48550/arXiv.1308.1122, 10.1016/j.laa.2014.02.012
Lankeit, Johannes ; Neff, Patrizio ; Nakatsukasa, Yuji. / The minimization of matrix logarithms : On a fundamental property of the unitary polar factor. in: Linear Algebra and Its Applications. 2014 ; Jahrgang 449. S. 28-42.
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