Norms on complex matrices induced by complete homogeneous symmetric polynomials

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  • Konrad Aguilar
  • Ángel Chávez
  • Stephan Ramon Garcia
  • Jurij Volčič

We introduce a remarkable new family of norms on the space of (Formula presented.) complex matrices. These norms arise from the combinatorial properties of symmetric functions, and their construction and validation involve probability theory, partition combinatorics, and trace polynomials in non-commuting variables. Our norms enjoy many desirable analytic and algebraic properties, such as an elegant determinantal interpretation and the ability to distinguish certain graphs that other matrix norms cannot. Furthermore, they give rise to new dimension-independent tracial inequalities. Their potential merits further investigation.

Original languageEnglish
JournalBulletin of the London Mathematical Society
Volume54
Issue number6
Pages (from-to)2078-2100
ISSN0024-6093
DOIs
Publication statusPublished - 2022

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© 2022 The Authors. Bulletin of the London Mathematical Society is copyright © London Mathematical Society.

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