Abstract
Let ‖ · ‖ be a unitarily invariant generalized matrix norm on Mn (C) the space of n-square complex matrices. Theorems are developed relating the Hadamard product (entrywise product) of two matrices A,BeMn (C) to the singular values of A and B. We conjecture that for any such norm. where A · B denotes the Hadamard product. For p ⩾ 1,1 ⩽ k ⩽ n, let where are the singular values of A. We prove that If 1<k<n we prove where Eq is the matrix with 1 in position (i,j) and zeros elsewhere. The case k = 1 is also discussed.
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