Lectures related to Vector bundle

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

Covers the properties of vectors, including commutativity, distributivity, and linearity.

Covers the definition of retraction, open submanifolds, local defining functions, tangent spaces, and Riemannian metrics.

Covers the representation and operations in coordinate space with points and vectors.

Covers the concept of kernel regression and K-nearest neighbors for making data linearly separable.

Explores adjoint functors, points fixes, orbits, and non-trivial actions in group theory.

Covers adjunctions, projective varieties, regularity, and valuative criteria in algebraic geometry.