Abstract
In this work, we study the set of strictly accretive matrices, that is, the set of matrices with positive definite Hermitian part, and show that the set can be interpreted as a smooth manifold. Using the recently proposed symmetric polar decomposition for sectorial matrices, we show that this manifold is diffeomorphic to a direct product of the manifold of (Hermitian) positive definite matrices and the manifold of strictly accretive unitary matrices. Utilizing this decomposition, we introduce a family of Finsler metrics on the manifold and characterize their geodesics and geodesic distances. Finally, we apply the geodesic distance to a matrix approximation problem and also give some comments on the relation between the introduced geometry and the geometric mean of strictly accretive matrices as defined by Drury [1].
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