ELA, Volume 8, pp. 26-46, March 2001, abstract.

Minimal Distortion Problems for Classes of Unitary Matrices

Vladimir Bolotnikov, Chi-Kwong Li, and Leiba Rodman
 
Given two chains of subspaces in the n-dimensional complex 
space, the set of those unitary matrices is studied that map 
the subspaces in the first chain onto the corresponding 
subspaces in the second chain, and minimize the value ||U-I|| 
for various unitarily invariant norms ||.|| on the algebra of 
complex n by n matrices. In particular, a formula for the 
minimum value ||U-I|| is given, and the set of all the unitary 
matrices in the set attaining the minimum is described, for 
the Frobenius norm. For other unitarily invariant norms, the 
results are obtained if the subspaces have special structure. 
Several related matrix minimization problems are also considered.