Group Actions: Examples

Related lectures (27)

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Explores orthogonality between vectors and subspaces, demonstrating practical implications in matrix operations.

Introduces abstract concepts in linear algebra, focusing on operations with vectors and matrices.

Covers kernels and images of linear transformations between vector spaces, illustrating properties and providing proofs.

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

Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.

Explores permutations preserving adjacency, linear transformations, groups, and sub-groups.

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

Explores group actions on spaces, including fixed points and non-trivial actions.

Explores linear operators, boundedness, and vector spaces with a focus on verifying bounded aspects.

Explains linear independence, bases, and dimension in vector spaces, including the importance of the order of vectors in a basis.