Extensions of the Hadamard determinant theorem
Let \(A=(a_{ij})\) be an n by n positive definite Hermitian matrix, and put \(h(A)=a_{11}a_{22}...a_{nn}\). If G is a permutation group of degree n with identity e and \(\chi\) is an irreducible complex character of G, define \(d(A)=\Sigma \chi(\sigma)\Pi a_{t\sigma(t)}\) where \(t=1,...,n\) and the sum is over all permutations \(\sigma\) in G. The author extends Hadamard's determinant theorem by showing that \(h(A)\geq [d(A^{1/n})/\chi(e)]^ n\) for all A.
scientific article; zbMATH DE number 3842055