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Non-Linear Interpolation of the Harmonic–Geometric–Arithmetic Matrix Means

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Bhatia, Lim, and Yamazaki conjectured that the Kubo–Ando extensions of means of numbers satisfy a norm minimality condition with respect to unitarily invariant norms. In this short note, we introduce… Click to show full abstract

Bhatia, Lim, and Yamazaki conjectured that the Kubo–Ando extensions of means of numbers satisfy a norm minimality condition with respect to unitarily invariant norms. In this short note, we introduce a symmetric Kubo–Ando mean and a non-Kubo–Ando extension that do not satisfy this property.

Keywords: non linear; interpolation harmonic; kubo ando; harmonic geometric; geometric arithmetic; linear interpolation

Journal Title: Lobachevskii Journal of Mathematics
Year Published: 2019

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