Titlebook: Matrix Information Geometry; Frank Nielsen,Rajendra Bhatia Book 2013 Springer-Verlag Berlin Heidelberg 2013 Audio Signal Processing.Covari

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https://doi.org/10.1007/978-3-642-30232-9Audio Signal Processing; Covariance matrix; Differential geometry of structured matrix; Fixed-Point SVD

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978-3-642-44847-8Springer-Verlag Berlin Heidelberg 2013

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Chronological

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Supremum/Infimum and Nonlinear Averaging of Positive Definite Symmetric Matriceshe supremum and infimum associated to the Löwner ellipsoids are computed as the asymptotic cases of nonlinear averaging using the original notion of counter-harmonic mean for PDS matrices. Properties of the three introduced approaches are explored in detail, including also some numerical examples.

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Exponential Barycenters of the Canonical Cartan Connection and Invariant Means on Lie Groupse group provides group geodesics which are completely consistent with the composition and inversion. With such a non-metric structure, the mean cannot be defined by minimizing the variance as in Riemannian Manifolds. However, the characterization of the mean as an exponential barycenter gives us an

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Information Geometry of Covariance Matrix: Cartan-Siegel Homogeneous Bounded Domains, Mostow/Berger used as natural space to compute “.-.” (. for “mean”, . for “median”) of covariance matrices via Karcher flow derived from Weiszfeld algorithm extension on Cartan-Hadamard manifold. This new mathematical framework will allow development of Ordered Statistic (OS) concept for Hermitian Positive Defin

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