ELA, Volume 3, pp. 4-12, January 1998, abstract.

Two Applications of a Bound on the Hadamard Product with a Cauchy Matrix

Roger A. Horn and Fuad Kittaneh

A fundamental bound for a Hadamard multiplier operator of Cauchy type
implies a known bound on the inverse of the operator $T:X\rightarrow
AX-XB$ as well as a general perturbation bound involving the unitary
factor in the polar decomposition; the latter bound leads to a
perturbation bound on the positive semidefinite factor.