Abstract
Let and Y be n× n matrices such that A and B are positive definite contractions. It is shown that if
and
then
Moreover, if
then
for
with
where
and
denote the Hilbert-Schmidt norm, the spectral matrix norm, the j th singular value, and the condition number of the n×n matrix T, respectively.
Acknowledgment
The authors would like to thank the editor and the referees for their comments and suggestions.