Lectures related to Tangent Spaces and Submersions

Explores Riemannian connections on manifolds, emphasizing smoothness and compatibility with the metric.

Covers elementary matrix operations and vector spaces, including properties and conditions for invertibility.

Covers the concept of 3D vector space, scalar product, bases, orthogonality, and projections.

Covers the definitions and properties of vector spaces, including axioms and examples.

Introduces Manopt, a toolbox for optimization on manifolds, focusing on solving optimization problems on smooth manifolds using the Matlab version.

Discusses gradients on Riemannian submanifolds and the construction of local frames.

Explores vector spaces, subspaces, bases, and linear combinations in R² and R³, including free and linked families.

Explores the orthogonal subspace in a vector space, demonstrating its properties and dimension determination.