Differential properties of spaces of symmetric real matrices
Alberto Dolcetti, Donato Pertici
TL;DR
This paper explores the geometric structure of the space of non-singular symmetric real matrices with the trace metric, highlighting the isometry group for positive definite matrices and revealing their differential geometric properties.
Contribution
It provides a detailed analysis of the differential geometry of symmetric matrix spaces and characterizes their isometry groups, especially for positive definite matrices.
Findings
Characterization of the differential geometric properties of symmetric matrix spaces
Full description of the isometry group for positive definite matrices
Insights into the structure of the manifold of non-singular symmetric matrices
Abstract
We study the differential geometric properties of the manifold of non-singular symmetric real matrices endowed with the trace metric; in case of positive definite matrices we describe the full group of isometries
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Taxonomy
TopicsAdvanced Topics in Algebra · Geometric Analysis and Curvature Flows · Advanced Differential Geometry Research