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W2986765257 abstract "Consider the Lie group of n×n complex unitary matrices U(n) endowed with the bi-invariant Finsler metric given by the spectral norm,‖X‖U=‖U⁎X‖∞=‖X‖∞ for any X tangent to a unitary operator U. Given two points in U(n), in general there exist infinitely many curves of minimal length. In this paper we provide a complete description of such curves and as a consequence we give an equivalent condition for uniqueness. Similar studies are done for the Grassmann manifolds. On the other hand, consider the cone of n×n positive invertible matrices Gl(n)+ endowed with the bi-invariant Finsler metric given by the trace norm,‖X‖1,A=‖A−1/2XA−1/2‖1 for any X tangent to A∈Gl(n)+. In this context, also exist infinitely many curves of minimal length. In this paper we provide a complete description of such curves proving first a characterization of the minimal curves joining two Hermitian matrices X,Y∈H(n). The last description is also used to construct minimal paths in the group of unitary matrices U(n) endowed with the bi-invariant Finsler metric‖X‖1,U=‖U⁎X‖1=‖X‖1for any X tangent to U∈U(n). We also study the set of intermediate points in all the previous contexts." @default.
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W2986765257 date "2020-03-01" @default.
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W2986765257 doi "https://doi.org/10.1016/j.jmaa.2019.123632" @default.
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