Norms on Complex Matrices Induced by Random Vectors

2022/11/15 by Ángel Chávez, Chávez, Ángel, Stephan Ramon Garcia +3
Computer Science · Mathematics · #15A60 #16R30 #47A30 #Advanced Algebra and Logic #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Probability (math.PR) #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.2211.07938

openalex publication_date 2022/11/15 · openalex created_date 2022/11/24 · openalex updated_date 2026/07/28

Abstract

We introduce a family of norms on the n × 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.

Related

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• Hunter's positivity theorem and random vector norms
• Norms on complex matrices induced by random vectors II: extension of weakly unitarily invariant norms
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• Positivity of Partitioned Hermitian Matrices with Unitarily Invariant Norms