An Arithmetic-Geometric-Harmonic Mean Inequality Involving Hadamard Products
نویسنده
چکیده
Given matrices of the same size, A = a ij ] and B = b ij ], we deene their Hadamard Product to be A B = a ij b ij ]. We show that if x i > 0 and q p 0 then the n n matrices q j # are positive deenite and relate these facts to some matrix valued arithmetic-geometric-harmonic mean inequalities-some of which involve Hadamard products and others unitarily invariant norms. It is known that if A is positive semideenite then maxfkA Bk : kBk 1g = maxa ii ; where k k denotes the spectral norm. We show that the converse of this statement is false and give a useful partial converse.
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