The Torus and Linear Groups

Related lectures (30)

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Explores injective and surjective linear transformations, kernel, image, and matrix operations.

Explores subrepresentations of the regular representation in group theory, emphasizing properties and isomorphism between subrepresentations.

Introduces the regular representation, a key tool for studying group actions on varieties.

Provides a recap of group theory, defining a group as a set with a multiplication operation.

Explores matrices, inverses, and their applications in linear algebra, emphasizing composition and transformation properties.

Explores properties and calculation tricks of determinants, including fixing rows/columns, expanding, and examples of determinant calculations.

Covers linear applications, matrices, transformations, and the principle of superposition.

Covers the isotopic decomposition of modules into simple components and their properties.

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

Explores eigenvalues, diagonalization, and matrix similarity, showcasing their importance and applications.