Norms on complex matrices induced by complete homogeneous symmetric polynomials
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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 language | English |
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Journal | Bulletin of the London Mathematical Society |
Volume | 54 |
Issue number | 6 |
Pages (from-to) | 2078-2100 |
ISSN | 0024-6093 |
DOIs | |
Publication status | Published - 2022 |
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© 2022 The Authors. Bulletin of the London Mathematical Society is copyright © London Mathematical Society.
ID: 317817409