Non-commutative Sylvester’s determinantal identity, preprint
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چکیده
Sylvester's identity is a classical determinantal identity with a straightforward linear algebra proof. We present a new, combinatorial proof of the identity, prove several non-commutative versions, and find a β-extension that is both a generalization of Sylvester's identity and the β-extension of the MacMahon master theorem.
منابع مشابه
Non-Commutative Sylvester's Determinantal Identity
Sylvester’s identity is a classical determinantal identity with a straightforward linear algebra proof. We present combinatorial proofs of several non-commutative extensions, and find a β-extension that is both a generalization of Sylvester’s identity and the β-extension of the quantum MacMahon master theorem.
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تاریخ انتشار 2007