50 research outputs found
Trace inequalities for completely monotone functions and Bernstein functions
We prove a matrix trace inequality for completely monotone functions and for
Bernstein functions. As special cases we obtain non-trivial trace inequalities
for the power function x->x^q, which for certain values of q complement
McCarthy's trace inequality and for others strenghten it.Comment: 16 page
A Singular Value Inequality for Heinz Means
We prove a matrix inequality for matrix monotone functions, and apply it to
prove a singular value inequality for Heinz means recently conjectured by X.
Zhan.Comment: 4 pages; Mistake in proof of Theorem 1 correcte
Spectral radius of Hadamard product versus conventional product for non-negative matrices
We prove an inequality for the spectral radius of products of non-negative
matrices conjectured by X. Zhan. We show that for all non-negative
matrices and , , where represents the Hadamard product.Comment: 4.1 page