Rearrangement inequalities for Hermitian matrices

Abstract: Hermitian matrices can be thought of as generalizations of real numbers. Many matrix inequalities, especially for Hermitian matrices, are derived from their scalar counterparts. In this paper, the Hardy–Littlewood–Pólya rearrangement inequality is extended to Hermitian matrices with respect to determinant, trace, Kronecker product, and Hadamard product. [ABSTRACT FROM AUTHOR]