Lectures related to Vector Subspaces and Canonical Forms

Covers kernels and images of linear transformations between vector spaces.

Covers scalar fields and level sets, focusing on the level set { x ∈ R³ | x² + x² + x₃ = 1}.

Explores the properties and applications of the dot product in vector spaces.

Covers the theory of orthogonal projection in vector spaces and its practical applications.

Covers matrix kernels, images, linear applications, independence, and bases in vector spaces.

Covers linear maps, matrices, and applications, including exercises on bases and invertibility.

Explores vector spaces, bases, and dimensions, including properties and proofs.