Let $S_n$ be the unit sphere with respect to the operator norm of the algebra of $n\times n$ complex matrices. We give a complete description of the form of surjections on $S_n$ which preserve the metric induced by a unitarily invariant strictly convex norm.
"Maps on the sphere of the algebras of matrices." Nihonkai Math. J. 26 (2) 121 - 125, 2015.