Generalizing the inequality per \((J_ 2\otimes M)\geq 2^ n[per(M)]^ 2\)
Let M be an \(n\times n\) positive semidefinite Hermitian matrix and \(W=(w_{ij})\) either a \(2\times 2\) real matrix such that \(w_{11}w_{22}\geq 0\) and \(w_{12}w_{21}\geq 0\) or a \(2\times 2\) Hermitian matrix such that \(w_{11}w_{22}\geq 0\). The author proves that per (W\(\otimes M)\geq (per W)^ n(per M)^ 2\). The cases of equality are discussed.
scientific article; zbMATH DE number 4051802