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Noncommutative Sylvester's determinantal identity
The electronic journal of combinatorics, Tome 14 (2007)

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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.
DOI : 10.37236/960
Classification : 05A30, 15A15
Mots-clés : quantum MacMahon master theorem 
Matjaž Konvalinka. Noncommutative Sylvester's determinantal identity. The electronic journal of combinatorics, Tome 14 (2007). doi: 10.37236/960
@article{10_37236_960,
     author = {Matja\v{z} Konvalinka},
     title = {Noncommutative {Sylvester's} determinantal identity},
     journal = {The electronic journal of combinatorics},
     year = {2007},
     volume = {14},
     doi = {10.37236/960},
     zbl = {1121.05012},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/960/}
}
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