Direct sum

Related lectures (31)

Page 3 of 4

Explores the isomorphism between Hom(A, B) and Hom(A, B) for any abelian group B.

Explores conjugation in groups, the direct product of groups, and the classification of finite abelian groups.

Explores the construction and properties of the free abelian group FAb(X) and its categorical extensions.

Covers the Orbit-Stabilizer theorem, conjugacy classes, and direct products in finite groups.

Covers group actions, conjugacy classes, centralizers, direct products, and finite abelian groups.

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

Covers the basis for irreducible representations and characters of direct product representations.

Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.

Covers the Jordan normal form and the decomposition of vector spaces by an endomorphism.

Covers the proof of the Classification Theorem for finite abelian groups, demonstrating the existence of a decomposition into cyclic groups.