completely reducible representation

completely reducible representation

[kəm¦plēt·lē ri¦düs·ə·bəl ‚rep·ri·zen′tā·shən]
(mathematics)
A representation of a group as a family of linear operators of a vector space V such that V is the direct sum of subspaces V1,…, Vn which are invariant under these operators, but V1,…, Vn do not have any proper closed subspaces which are also invariant under these operators. Also known as semisimple representation.
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