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completely reducible representation

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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 spaceVsuch thatVis the direct sum of subspacesV1,…,Vnwhich are invariant under these operators, butV1,…,Vndo not have any proper closed subspaces which are also invariant under these operators. Also known as semisimple representation.


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