Comptes Rendus
no. 5
Algebra/Mathematical analysis
Confluent Vandermonde matrices and divided differences over quaternions
[Matrices de Vandermonde confluentes et différences divisées sur les quaternions]

Présenté par : the Editorial Board

Vladimir Bolotnikov1
1 Department of Mathematics, College of William and Mary, Williamsburg, VA 23187-8795, USA
Comptes Rendus. Mathématique, Volume 353 (2015) no. 5, pp. 391-395.

Nous introduisons la notion de matrice de Vandermonde confluente sur les quaternions et nous calculons son rang. Ceci étend les résultats de T.Y. Lam (A general theory of Vandermonde matrices, Expo. Math. 4 (3) (1986) 193–215). Ensuite, nous montrons une formule de représentation d'ordre supérieur pour les différences divisées de polynômes à coefficients quaternions, généralisant un résultat de G. Gentili et D.C. Struppa (A new theory of regular functions of a quaternionic variable, Adv. Math. 216 (1) (2007) 279–301).

We introduce the notion of a confluent Vandermonde matrix over quaternions and present the formula to compute its rank. This extends a result of T.Y. Lam (A general theory of Vandermonde matrices, Expo. Math. 4 (3) (1986) 193–215). Another contribution is the representation formula for divided differences of quaternion polynomials which extends a result of G. Gentili and D.C. Struppa (A new theory of regular functions of a quaternionic variable, Adv. Math. 216 (1) (2007) 279–301).

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2015.02.004
Vladimir Bolotnikov 1

1 Department of Mathematics, College of William and Mary, Williamsburg, VA 23187-8795, USA 
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     title = {Confluent {Vandermonde} matrices and divided differences over quaternions},
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     pages = {391--395},
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     year = {2015},
     doi = {10.1016/j.crma.2015.02.004},
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Vladimir Bolotnikov. Confluent Vandermonde matrices and divided differences over quaternions. Comptes Rendus. Mathématique, Volume 353 (2015) no. 5, pp. 391-395. doi : 10.1016/j.crma.2015.02.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.02.004/

[1] V. Bolotnikov Polynomial interpolation over quaternions, J. Math. Anal. Appl., Volume 421 (2015) no. 1, pp. 567-590

[2] G. Gentili; D.C. Struppa A new theory of regular functions of a quaternionic variable, Adv. Math., Volume 216 (2007) no. 1, pp. 279-301

[3] D. Kalman The generalized Vandermonde matrix, Math. Mag., Volume 57 (1984) no. 1, pp. 15-21

[4] T.Y. Lam A general theory of Vandermonde matrices, Expo. Math., Volume 4 (1986) no. 3, pp. 193-215

[5] T.Y. Lam; A. Leroy Vandermonde and Wronskian matrices over division rings, J. Algebra, Volume 119 (1988) no. 2, pp. 308-336

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