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Similarity classes of 3×3 matrices over a local principal ideal ring. (English) Zbl 1176.15013
In general, the classification problem of similarity classes in n by n matrices over rings other than fields is a highly nontrivial question. In this article, similarity classes of three by three matrices over a local principal ideal commutative ring are analyzed. When the residue field is finite, a generating function for the number of similarity classes for all finite quotients of the ring is computed explicitly.
MSC:
15A21Canonical forms, reductions, classification
15A54Matrices over function rings
15A33Matrices over special rings