Procrustes problems in Riemannian manifolds of positive definite matrices

Rajendra Bhatia (1) , Marco Congedo (2)

1 Ashoka University
2 GIPSA-VIBS - GIPSA - Vision and Brain Signal Processing

We consider the manifold of positive definite matrices endowed with the Fisher Riemannian metric and some other distances commonly used in information theory. We show that for each of them the best approximant to A from the unitary orbit of another matrix B commutes with A.

Domaines: Traitement du signal et de l'image [eess.SP]; Géométrie différentielle [math.DG]

Rajendra Bhatia, Marco Congedo. Procrustes problems in Riemannian manifolds of positive definite matrices. Linear Algebra and its Applications, 2019, 563, pp.440-445. ⟨10.1016/j.laa.2018.11.009⟩. ⟨hal-02023293⟩