Lectures related to Functional Analysis I: November 18, 2021

Covers orthogonal families and projections in vector spaces, including the Gram-Schmidt process.

Introduces partial orderings, lattices, and lexicographic orderings on Cartesian products.

Explores norms and bounded operators in functional analysis, demonstrating their properties and applications.

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

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

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

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

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