Bases in Known Dimension Space

Covers the concept of the dimension of a subspace in a finite-dimensional vector space.

Explores equivalence in vector spaces, covering conditions for statements to be considered equivalent and properties of algebraic bases.

Introduces linear applications, span, kernels, and images in vector spaces with illustrative examples and theorems.

Explores orthogonality between vectors and subspaces, demonstrating practical implications in matrix operations.

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