Notes on Cartesian symmetry classes and generalized trace functions (Q1124867)

Generalized trace functions (defined in earlier works) of a complex matrix, symmetrizers on the \(m\)-fold Cartesian product space of an \(n\)-dimensional unitary vector space and induced operators on Cartesian symmetry classes are investigated. Conditions for various properties of symmetrizers (normal, unitary, Hermitian, positive semi-definite, positive definite ones) are determined. A theorem for the matrix norm using properties of generalized trace functions is derived.