Norms on complex matrices induced by complete homogeneous symmetric polynomials

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

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

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
DOIs
StateAccepted/In press - 1 Jan 2022
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics (all)

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