Ela Minimal Distortion Problems for Classes of Unitary Matrices ∗
نویسنده
چکیده
Given two chains of subspaces in C, 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 − In‖ for various unitarily invariant norms ‖ · ‖ on Cn×n. In particular, a formula for the minimum value ‖U − In‖ 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.
منابع مشابه
Minimal distortion problems for classes of unitary matrices
Given two chains of subspaces in C, we study the set of unitary matrices that map the subspaces in the first chain onto the corresponding subspaces in the second chain, and minimize the value ‖U− In‖ for various unitarily invariant norms ‖ · ‖ on Cn×n. In particular, we give formula for the minimum value ‖U − In‖, and describe the set of all the unitary matrices in the set attaining the minimum...
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