Abstract
Let A be a matrix in Cn×n and let UΣV* be its singular value decomposition. The authors prove that for each 1⩽k⩽n the set S(k)1={S∈Cn×n:∑1⩽j1<…<jk⩽nσj1(S)σj2(S)…σjk(S)⩽1} is a Chebyshev set in Cn×n endowed with the spectral norm and that the metric projection is globally Lipschitz-continuous.
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