ELA ON INEQUALITIES INVOLVING THE HADAMARD PRODUCT OF MATRICES

Abstract. Recently, the authors established a number of inequalities involving integer powers of the Hadamard product of two positive denite Hermitian matrices. Here these results are extended in two ways. First, the restriction to integer powers is relaxed to include all real numbers not in the open interval (1; 1). Second, the results are extended to the Hadamard product of any nite number of Hermitian positive denite matrices