Lectures related to Linear Maps and Bases: The Rank Theorem

Covers the Rank Theorem in linear algebra, focusing on vector spaces and linear applications.

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

Introduces the kernel of a linear application and its properties.

Covers dimension theorems for linear transformations, bijectivity, isomorphism, dual spaces, and canonical applications.

Explores subspaces in linear algebra and transformations, including kernels and images of linear transformations.

Explains linear independence, bases, and dimension in vector spaces, including the importance of the order of vectors in a basis.