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Norms on Complex Matrices Induced by Random Vectors
Ángel Chávez, Stephan Ramon Garcia, Jackson Hurley · 2022-11-15 · via math.PR updates on arXiv.org

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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