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- W2056595410 abstract "A norm or seminorm on ∥ · ∥ on Rn is permutation invariant if ∥Px∥ = ∥x∥ for all n × n permutation matrices P and for all x ∈ Rn. We present a systematic study of permutation invariant seminorms. Their relations with other types of norms on matrices are discussed. In addition, we consider a special class of permutation invariant seminorms, the c-radii, defined and denoted by Rc(x) = max{|ctPx| : P a permutation} for any given c ∈Rn. It is shown that Rc are the building blocks of all permutation invariant seminorms. If the entries of c are not all equal and their sum is not 0, then Rc is a norm on Rn. For such Rc, we study their norm properties and characterize their isometry groups." @default.
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- W2056595410 date "1995-04-01" @default.
- W2056595410 modified "2023-09-29" @default.
- W2056595410 title "Permutation invariant norms" @default.
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- W2056595410 doi "https://doi.org/10.1016/0024-3795(93)00198-9" @default.
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