Direct Sums of Abelian Groups

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Representation Theory: Algebras and Homomorphisms

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

Group Direct Sums in Group Theory

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

Polynomials: Operations and Properties

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

Categorical Perspective: Abelian Groups

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

Concrete Categories

Covers concrete categories with sets and structures, including Ens, Gr, Ab, and Vectk.

Hom Functor: Abelian Groups

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

Free Abelian Groups and Homomorphisms

Explores free abelian groups, homomorphisms, and exact sequences in the context of different categories.

Orthogonal Vectors and Projections

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

Direct Sums: Abelian Groups

Explores the concept of direct sums in abelian groups, emphasizing the universal property and homomorphisms.

Group representations constructions

Explores the construction of group representations through various methods and provides an illustrative example using the standard representation of sr2 on c2.