Foundations of Riemannian Geometry for Riemannian Optimization: A Monograph with Detailed Derivations

ArXi:2605.02279v1 Announce Type: cross Riemannian geometry provides the fundamental framework for optimization on nonlinear spaces such as matrix manifolds, which arise in machine learning, signal processing, and robotics. While the underlying theory is classical, existing literature often presents results at a high level of abstraction, omitting the detailed coordinate-level derivations required for implementation and algorithm development.