Lecture
Embedded Submanifolds: Stiefel Manifold
Related lectures (35)
Differential Equations Solutions
Covers solutions of differential equations with initial conditions and boundedness concepts.
Riemannian metrics and gradients: Examples and Riemannian submanifoldsMOOC: Introduction to optimization on smooth manifolds: first order methods
Explores Riemannian metrics on manifolds and the concept of Riemannian submanifolds in Euclidean spaces.
Fixed-Rank Manifold: Tangent Spaces and Local Defining Functions
Explores fixed-rank matrices as an embedded submanifold, focusing on constructing local defining functions and efficiently computing tangent vectors.
Fundamental Solutions
Covers the concept of fundamental solutions in the context of differential operators.
Smooth maps and differentials: Smooth mapsMOOC: Introduction to optimization on smooth manifolds: first order methods
Explores smooth maps between submanifolds, discussing smoothness criteria and composition preservation.