Lectures related to Norms and Orthogonality

Linear Algebra: Lecture Notes

Covers determining vector spaces, calculating kernels and images, defining bases, and discussing subspaces and vector spaces.

Orthogonal Bases in Vector Spaces

Covers the concept of orthogonal bases in vector spaces and Pythagorean theorem applications.

Linear Transformations: Kernels and Images

Covers kernels and images of linear transformations between vector spaces, illustrating properties and providing proofs.

Matrix Operations and Orthogonality

Covers matrix operations, scalar product, orthogonality, and bases in vector spaces.

Orthogonality and Subspaces

Explores orthogonality, vector norms, and subspaces in Euclidean space, including determining orthogonal complements and properties of subspaces and matrices.

Vector Calculus in 3D

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

Tangent Spaces and Submersions

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