Lectures related to Vector Space Dimension and Bases

Introduces orthogonal families, orthonormal bases, and projections in linear algebra.

Explores bases in vector spaces, including linear combinations, orthogonal bases, and basis transformations using rotation matrices.

Covers scalar products, orthogonal vectors, norms, and projections in vector spaces, emphasizing orthonormal families of vectors.

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

Covers isomorphism, dimension, bases, and rank in linear transformations between vector spaces.

Covers the properties and operations of vector spaces, including addition and scalar multiplication.