Fixed-Rank Manifold: Tangent Spaces and Local Defining Functions

Related lectures (30)

Page 1 of 3

Covers classical and quantum computational complexity concepts and implications.

Covers smooth maps on manifolds, defining functions, tangent spaces, and differentials.

Covers retractions, tangent bundles, and embedded submanifolds on manifolds with proofs and examples.

Explores the transition from embedded to general manifolds, upgrading foundational concepts and discussing mathematical reasons for both approaches.

Covers embedded submanifolds, Stiefel manifold, tangent spaces, and differential ranks.

Explores algorithm complexity, analyzing efficiency and worst-case scenarios of sorting algorithms.

Explores Projection Pursuit Regression for nonlinear modeling and the trade-offs with interpretability in neural networks.

Covers the Subset Sum problem and the efficient LLL algorithm for finding solutions in lattice basis reduction.

Delves into challenges of learning from probabilistic models, covering computational complexity, data reconstruction, and statistical gaps.

Covers tangent spaces and submersions in differential geometry, emphasizing vector spaces and differentiable structures.