Non-commutative Sylvester's determinantal identity
Combinatorics
2007-05-23 v1
Abstract
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 -extension that is both a generalization of Sylvester's identity and the -extension of the MacMahon master theorem.
Cite
@article{arxiv.math/0703213,
title = {Non-commutative Sylvester's determinantal identity},
author = {Matjaz Konvalinka},
journal= {arXiv preprint arXiv:math/0703213},
year = {2007}
}
Comments
28 pages, 8 figures