Non-Commutative Sylvester's Determinantal Identity

  • MatjaĆŸ Konvalinka

Abstract

Sylvester's identity is a classical determinantal identity with a simple linear algebra proof. We present combinatorial proofs of several non-commutative extensions, and find a $\beta$-extension that is both a generalization of Sylvester's identity and the $\beta$-extension of the quantum MacMahon master theorem.

Published
2007-05-31
Article Number
R42