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Explore a 17-minute mathematics lecture from the ESI's Thematic Programme on "Infinite-dimensional Geometry" that delves into the geometric applications of correlation matrices in neuroimaging. Learn how Riemannian metrics offer alternatives to traditional Euclidean approaches when working with symmetric positive definite matrices. Discover various methods for applying differentiable structures to correlation matrices, particularly in the context of brain connectivity analysis. Examine recent developments in Riemannian metrics for full-rank correlation matrices and their role in non-linear space statistics. Study the quotient geodesics of the Frobenius metric on covariance matrices and their application to full-rank correlation matrices. See practical applications of these mathematical concepts in analyzing brain connectomes using resting-state fMRI data.
