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Noncommutative determinants, Cauchy–Binet formulae, and Capelli-type identities I. Generalizations of the Capelli and Turnbull identities
1
Washington Place New York, NY 10003 USA
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3
Publication type: Journal Article
Publication date: 2009-08-07
scimago Q1
wos Q2
SJR: 0.897
CiteScore: 1.3
Impact factor: 0.7
ISSN: 10778926, 10971440
DOI:
10.37236/192
Computational Theory and Mathematics
Applied Mathematics
Theoretical Computer Science
Discrete Mathematics and Combinatorics
Geometry and Topology
Abstract
We prove, by simple manipulation of commutators, two noncommutative generalizations of the Cauchy–Binet formula for the determinant of a product. As special cases we obtain elementary proofs of the Capelli identity from classical invariant theory and of Turnbull's Capelli-type identities for symmetric and antisymmetric matrices.
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11
Total citations:
11
Citations from 2024:
2
(18.18%)
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Caracciolo S. et al. Noncommutative determinants, Cauchy–Binet formulae, and Capelli-type identities I. Generalizations of the Capelli and Turnbull identities // Electronic Journal of Combinatorics. 2009. Vol. 16. No. 1. R103
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Caracciolo S., Sokal A. D., Sportiello A. Noncommutative determinants, Cauchy–Binet formulae, and Capelli-type identities I. Generalizations of the Capelli and Turnbull identities // Electronic Journal of Combinatorics. 2009. Vol. 16. No. 1. R103
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TY - JOUR
DO - 10.37236/192
UR - https://www.combinatorics.org/ojs/index.php/eljc/article/view/v16i1r103
TI - Noncommutative determinants, Cauchy–Binet formulae, and Capelli-type identities I. Generalizations of the Capelli and Turnbull identities
T2 - Electronic Journal of Combinatorics
AU - Caracciolo, Sergio
AU - Sokal, Alan D.
AU - Sportiello, Andrea
PY - 2009
DA - 2009/08/07
PB - Electronic Journal of Combinatorics
IS - 1
VL - 16
SN - 1077-8926
SN - 1097-1440
ER -
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BibTex (up to 50 authors)
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@article{2009_Caracciolo,
author = {Sergio Caracciolo and Alan D. Sokal and Andrea Sportiello},
title = {Noncommutative determinants, Cauchy–Binet formulae, and Capelli-type identities I. Generalizations of the Capelli and Turnbull identities},
journal = {Electronic Journal of Combinatorics},
year = {2009},
volume = {16},
publisher = {Electronic Journal of Combinatorics},
month = {aug},
url = {https://www.combinatorics.org/ojs/index.php/eljc/article/view/v16i1r103},
number = {1},
pages = {R103},
doi = {10.37236/192}
}