Lectures related to Complemented subspace

Explores polynomial operations, properties, and subspaces in vector spaces.

Introduces orthogonality between vectors, angles, and orthogonal complement properties in vector spaces.

Covers the concept of the sum of vector subspaces in an IR-vector space.

Explores the concept of free abelian groups as an important left adjoint functor.

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

Covers weak derivatives, their properties, and applications in functional analysis.

Covers the existence and uniqueness of direct sums in abelian groups.

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

Explores Wedderburn's theorem, group algebras, and Maschke's theorem in the context of finite dimensional simple algebras and their endomorphisms.

Covers the weak formulation of elliptic partial differential equations and the uniqueness of solutions in Hilbert space.

Covers the concept of orthogonal complement and projection in vector spaces.

Covers self-similar groups and automorphisms of rooted trees, exploring residually finite groups and congruence subgroups.

Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.

Covers the basics of linear algebra, emphasizing the identification of subspaces through key properties.

Demonstrates the existence of direct sums of abelian groups and covers propositions and proofs related to their uniqueness.

Explores direct sums in abelian groups, emphasizing existence and uniqueness.

Explores the arithmetic of direct sums in group theory, discussing conditions for equality.

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

Explores direct sums in group theory, focusing on abelian groups and their implications.

Explores abelian groups from a categorical perspective, discussing the coproduct construction.