  Correlation matrices are used in many domains of neurosciences such as fMRI,
EEG, MEG. However, statistical analyses often rely on embeddings into a
Euclidean space or into Symmetric Positive Definite matrices which do not
provide intrinsic tools. The quotient-affine metric was recently introduced as
the quotient of the affine-invariant metric on SPD matrices by the action of
diagonal matrices. In this work, we provide most of the fundamental Riemannian
operations of the quotient-affine metric: the expression of the metric itself,
the geodesics with initial tangent vector, the Levi-Civita connection and the
curvature.
