Norms on complex matrices induced by complete homogeneous symmetric polynomials
Norms on complex matrices induced by complete homogeneous symmetric polynomials
We introduce a remarkable new family of norms on the space of n × n $n \times n$ complex matrices. These norms arise from the combinatorial properties of symmetric functions, and their construction and validation involve probability theory, partition combinatorics, and trace polynomials in non-commuting variables. Our norms enjoy many …