Abstract
We first present an inequality for the Frobenius norm of the Hadamard product of two any square matrices and positive semidefinite matrices. Then, we obtain a trace inequality for products of two positive semidefinite block matrices by using block matrices.
Highlights
Introduction and PreliminariesLet Mm,n denote the space of m × n complex matrices and write Mn ≡ Mn,n
We first present an inequality for the Frobenius norm of the Hadamard product of two any square matrices and positive semidefinite matrices
We present an inequality for Frobenius norm of the power of Hadamard product of two matrices
Summary
Introduction and PreliminariesLet Mm,n denote the space of m × n complex matrices and write Mn ≡ Mn,n. We first present an inequality for the Frobenius norm of the Hadamard product of two any square matrices and positive semidefinite matrices. We obtain a trace inequality for products of two positive semidefinite block matrices by using 2 × 2 block matrices. Let Mm,n denote the space of m × n complex matrices and write Mn ≡ Mn,n. Let A and B be two Hermitian matrices of the same size.
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