Non-commutative Sylvester's determinantal identity

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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.
28 pages, 8 figures

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Combinatorics, 05A30, 15A15

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http://salesiana.dossiersoluciones.com/handle/123456789/125310

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0703213
 http://arxiv.org/abs/math/0703213

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arXiv