Non-commutative Sylvester's determinantal identity

Details Non-commutative Sylvester's determinantal identity Non-commutative Sylvester's determinantal identity

2007-03-08

arxiv.org/abs/math/0703213v1

Mathematics

Combinatorics

28 pages, 8 figures

Scientific paper

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
$\beta$-extension that is both a generalization of Sylvester's identity and the
$\beta$-extension of the MacMahon master theorem.

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