Representation Theory
Explore linear actions; characters and decomposition; construction and lie theory. Concepts and connections are available independently of video coverage.
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Invariant subspaces
An invariant subspace is preserved by every transformation in a representation.
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Group representations
A group representation is a homomorphism into invertible linear transformations.
Irreducible representations
An irreducible representation has no nonzero proper invariant subspace.
Characters
A finite-dimensional representation's character assigns the trace of each represented element.
Complete reducibility
A representation is completely reducible when it is a direct sum of irreducible representations.
Induced representations
A subgroup representation can be extended through an induction construction to the larger group.
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