Applications of the duality method to generalizations of the Jordan canonical form
نویسنده
چکیده
We show how Ptak’s duality method leads to short proofs of two extensions of the Jordan canonical form, viz. the normal form for a matrix over an arbitrary (not necessarily algebraically closed) field under similarity and the canonical form for a pair of matrices under contragredient equivalence. The duality method is summarized in the following. Lemma. Let V be a finite-dimensional space over a field F , let A : V → V be a linear map, and S ⊂ V be an A-invariant subspace of V . If T ⊂ V ∗ is an A-invariant subspace of the dual V ∗ of V such that
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