Embedded Submanifolds: Stiefel Manifold

Related lectures (32)

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Explores upgrading foundations from embedded to general manifolds in optimization, discussing smooth sets and tangent vectors.

Explores smooth functions on manifolds, emphasizing continuity and atlas topologies.

Covers the definitions of differentiable and derivable functions and their geometric interpretation.

Explores tangent spaces as free movement directions on submanifolds, offering a geometrically satisfying linearization notion.

Explores finding the equation of the tangent line to a function's graph at a point.

Covers Riemannian metrics, gradients, vector fields, and inner products on manifolds.

Explores Riemannian metrics on manifolds and the concept of Riemannian submanifolds in Euclidean spaces.

Covers the Grassmann manifold and retractions on submanifolds.

Covers Newton's method on Riemannian manifolds, focusing on second-order optimality conditions and quadratic convergence.

Explores smooth manifolds through diffeomorphisms and embedded submanifolds in a linear space.