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Norms on complex matrices induced by random vectors
Published online by Cambridge University Press: 23 December 2022
Abstract
We introduce a family of norms on the $n \times n$ complex matrices. These norms arise from a probabilistic framework, and their construction and validation involve probability theory, partition combinatorics, and trace polynomials in noncommuting variables. As a consequence, we obtain a generalization of Hunter’s positivity theorem for the complete homogeneous symmetric polynomials.
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- © The Author(s), 2022. Published by Cambridge University Press on behalf of The Canadian Mathematical Society
Footnotes
S.R.G. was partially supported by the NSF (Grant No. DMS-2054002).
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