Reducible representation ↩

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created: 2021-10-19 13:32:26
modified: 2022-01-10 04:13:04

For a representation there exists an

so that:

Definition

group, representation, then is reducible if the matrices in the set have a common nontrivial invariant subspace, i.e. there exists an so that for all , will be of this hypermatrix shape:

The invariant subspaces

The invariant subspace of the matrices is then the column (hyper)vector
And for the matrices:

Reducible representation ↩

Definition

The invariant subspaces

See also