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volume 16 issue 1 publication number R103

Noncommutative determinants, Cauchy–Binet formulae, and Capelli-type identities I. Generalizations of the Capelli and Turnbull identities

Publication typeJournal Article
Publication date2009-08-07
scimago Q1
wos Q2
SJR0.897
CiteScore1.3
Impact factor0.7
ISSN10778926, 10971440
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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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
GOST all authors (up to 50) Copy
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
RIS |
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RIS Copy
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 -
BibTex
Cite this
BibTex (up to 50 authors) Copy
@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}
}