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Jordan Decomposition Theorem
Definition: [Vector space form]: Let T be a linear operator on a finite-dimensional complex vector space V. There is a basis B of V such that the matrix of T with respect to B has Jordan form. [Matrix form]: Let A be an nxn complex matrix. There is an invertible matrix P such that (P^-1)AP has Jordan form.
Source: Algebra, second edition by Michael Artin