The Schur Product Theorem in the Block Case

D. Choudhury
1990 Proceedings of the American Mathematical Society  
Let H be a positive semi-definite mn-by-mn Hermitian matrix, partitioned into m2 «-square blocks H¡j, i,j = \,...,m. We denote this by H = [H¡j]. Consider the function /: M" -* Mr given by f{X) = Xk (ordinary matrix product) and denote Hf = [f(H¿j)]. We shall show that if H is positive semi-definite then under some restrictions on H¡j , Hf is also positive semi-definite. This generalizes familar results for Hadamard and ordinary products.
doi:10.2307/2047941 fatcat:czii26w5zjgdtodxz72juf6g7u