The Alpha-Procrustes geometry at alpha=1 produces Riemannian Hessians whose eigenvalues are uniformly bounded independent of the SPD matrix condition number, provided the Euclidean Hessian satisfies uniform spectral bounds.
Princeton university press (2009)
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Riemannian Optimization over Symmetric Positive Definite Matrices with the Alpha-Procrustes Geometry
The Alpha-Procrustes geometry at alpha=1 produces Riemannian Hessians whose eigenvalues are uniformly bounded independent of the SPD matrix condition number, provided the Euclidean Hessian satisfies uniform spectral bounds.