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].

在这项工作中，我们研究了严格增生矩阵集，即具有正定 Hermitian 部分的矩阵集，并表明该集可以解释为光滑流形。使用最近提出的扇形矩阵的对称极坐标分解，我们表明该流形微分同胚于（厄米特）正定矩阵流形与严格增生酉矩阵流形的直积。利用这种分解，我们在流形上引入了一系列 Finsler 度量，并描述了它们的测地线和测地线距离。最后，我们将测地线距离应用于矩阵近似问题，并对引入的几何与 Drury [1] 定义的严格增生矩阵的几何平均值之间的关系给出了一些评论。