The Torus and Linear Groups

Related lectures (30)

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Covers scaled matrices, ladder matrices, and the Gauss method for matrix operations.

Covers matrix transposition, rank, and basis change in linear algebra, exploring invertibility criteria and basis relationships.

Explores the unique determination of homomorphisms by differentials and the intersection of closed subgroups' Lie algebras.

Explores self-similar groups acting on rooted trees and their properties.

Introduces characters as group homomorphisms from linear algebraic groups to multiplicative groups.

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

Covers elementary row operations, equivalent matrices, invertibility, and bases in linear algebra.

Showcases examples of group actions on vector spaces and topological spaces.

Covers fundamental concepts in linear algebra, including linear equations, matrix operations, determinants, and vector spaces.

Explores the properties and applications of triangular matrices in linear algebra.