Linear algebraic group

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Related lectures (27)

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Commutative algebraic groups

Covers the properties of commutative linear algebraic groups and their elements.

Diagonalizable Groups

Explores the concept of diagonalizable groups and their properties in linear algebraic groups.

Jordan decomposition: Lie algebra

Delves into the Jordan decomposition in Lie algebras of linear algebraic groups.

Representation Theory: Algebras and Homomorphisms

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

Vector Spaces: Properties and Examples

Explores vector spaces, focusing on properties, examples, and subspaces within a practical exercise on polynomials.

Quotient Criterion

Explores a criterion for computing quotients in algebraic geometry, emphasizing the importance of normality and g-invariant morphisms.

Quotients: Geometrical Properties

Delves into the geometrical properties of quotients by linearly reductive groups, emphasizing the uniqueness of closed orbits and the concept of a geometric quotient.

Convex Optimization: Convex Functions

Covers the concept of convex functions and their applications in optimization problems.

Linear Models: Least Squares

Explores linear models, least squares, Gaussian vectors, and model selection methods.

The Coordinate Ring of a Linearly Reductive Group

Covers the properties of the coordinate ring of a linearly reductive group.