Norms on complex matrices induced by complete homogeneous symmetric polynomials
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Norms on complex matrices induced by complete homogeneous symmetric polynomials. / Aguilar, Konrad; Chávez, Ángel; Garcia, Stephan Ramon; Volčič, Jurij.
I: Bulletin of the London Mathematical Society, Bind 54, Nr. 6, 2022, s. 2078-2100.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Norms on complex matrices induced by complete homogeneous symmetric polynomials
AU - Aguilar, Konrad
AU - Chávez, Ángel
AU - Garcia, Stephan Ramon
AU - Volčič, Jurij
N1 - Publisher Copyright: © 2022 The Authors. Bulletin of the London Mathematical Society is copyright © London Mathematical Society.
PY - 2022
Y1 - 2022
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85130954048&partnerID=8YFLogxK
U2 - 10.1112/blms.12679
DO - 10.1112/blms.12679
M3 - Journal article
AN - SCOPUS:85130954048
VL - 54
SP - 2078
EP - 2100
JO - Bulletin of the London Mathematical Society
JF - Bulletin of the London Mathematical Society
SN - 0024-6093
IS - 6
ER -
ID: 317817409