Concept

Complemented subspace

Related lectures (28)

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.

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

Explores orthogonal complement and projection theorems in vector spaces.

Explores the Hom functor for abelian groups and its relation to direct sums.

Covers norm, scalar product, and perpendicularity in R^n, including the theorem of Pythagoras and orthogonal complements.