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.

• Type: Journal
• Year: 2007
• Where: COMBINATORICS
• Authors: Matjaz Konvalinka
• Keywords: Classical Determinantal Identity, COMBINATORICS 2007, Straightforward Linear Algebra, Sylvester’s Identity