Unitarily invariant generalized matrix norms and hadamard products
Marvin D. Marcus, Kent Kidman, Markus Sandy · Linear and Multilinear Algebra · 1984
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,BεMn (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