Abstract
Let Ω be a symmetric cone. In this note, we introduce Hilbert’s projective metric on Ω in terms of Jordan algebras and we apply it to prove that, given a linear invertible transformation g such that g(Ω) = Ω and a real number p, |p| > 1, there exists a unique element x ∈ Ω satisfying g(x) = x p.
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Koufany, K. Application of Hilbert’s Projective Metric on Symmetric Cones. Acta Math Sinica 22, 1467–1472 (2006). https://doi.org/10.1007/s10114-005-0755-6
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DOI: https://doi.org/10.1007/s10114-005-0755-6