Norms on Complex Matrices Induced by Random Vectors

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.

18 pages