Lectures related to Linear Algebra: Subspaces and Transformations

Covers linear algebra basics, including matrices, change of basis, and invertible matrices.

Explores solutions of linear equations, null spaces, subspaces, vector spaces, linear independence, bases, and dimensions.

Covers vector spaces, subspaces, kernel, image, linear independence, and bases in linear algebra.

Covers the concepts of kernel and image of a linear transformation and their relationship with the rank of the matrix.

Covers linear independence, bases, and coordinate systems with examples and theorems.

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

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

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