Lectures related to Bases in Known Dimension Space

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

Explores orthogonality, norms, and distances in vector spaces for solving linear systems.

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

Explains the dimension of a sum of vector subspaces in a vector space.

Covers the concept of orthogonal complement in Rn and related propositions and theorems.

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

Explores bases, dimensions, and matrix ranks in vector spaces with practical examples and proofs.

Explores counter examples and proofs in vectorial spaces, emphasizing rigorous reasoning.

Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.