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.