Some remarks on the norm upper bounds associated with the generalized polar decompositions of matrices

A correction, along with an improvement, is made on a recent joint work of the second author and the third author. An optimal perturbation bound is also clarified for certain 2 x 2 Hermitian matrices.

Automated summary

A correction and improvement are made on a recent joint work by the second and third authors. An optimal perturbation bound is also clarified for certain 2 x 2 Hermitian matrices.