The Regular Representation

Related lectures (27)

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

Explores the embedding of chi-varieties into vector spaces with linear actions.

Explores the differential of group actions on vector spaces and the behavior of orbit maps.

Generalizes group actions beyond sets, providing a comprehensive framework for various mathematical contexts.

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

Introduces Lie algebras, vector spaces with a special bracket operation.

Explores Schur's lemma and its applications in representations of an associative algebra over an algebraically closed field.

Covers determining vector spaces, calculating kernels and images, defining bases, and discussing subspaces and vector spaces.

Covers the basics of linear algebra, including linear maps, bases, and matrix operations.

Covers matrix kernels, images, linear applications, independence, and bases in vector spaces.