Geodesic
Norms on complex matrices induced by random vectors
Canadian mathematical bulletin, Tome 66 (2023) no. 3, pp. 808-826

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DOI

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.
DOI : 10.4153/S0008439522000741
Mots-clés : Norm, symmetric polynomial, partition, trace, positivity, convexity, expectation, complexification, trace polynomial, probability distribution 
Chávez, Ángel; Garcia, Stephan Ramon; Hurley, Jackson. Norms on complex matrices induced by random vectors. Canadian mathematical bulletin, Tome 66 (2023) no. 3, pp. 808-826. doi: 10.4153/S0008439522000741
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     title = {Norms on complex matrices induced by random vectors},
     journal = {Canadian mathematical bulletin},
     pages = {808--826},
     year = {2023},
     volume = {66},
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     doi = {10.4153/S0008439522000741},
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