(Received: 2022-03-11
, Revised: 2022-04-05
)
(Received: 2022-03-11
, Revised: 2022-04-05
)
Askold Khovanskii, FRSC, University of Toronto, Toronto, Canada; e-mail: askold@math.toronto.edu
Sushil Singla, Department of Mathematics, Shiv Nadar University, Greater Noida, India 201314; e-mail: ss774@snu.edu.in
Aaron Tronsgard, University of Toronto, Toronto, Canada; e-mail: tronsgar@math.utoronto.ca
Abstract/Résumé:
We reconsider the theory of Lagrange interpolation polynomials with multiple interpolation points and apply it to linear algebra. In particular, we show that one can evaluate a meromorphic function at a matrix, using only an interpolation polynomial.
On reconsidère la thèorie des polynômes d’interpolation de Lagrange et l’applique à l’algèbre linéaire. En particulier, on peut évaluer une fonction méromorphe à une matrice seulement avec un polynôme d’interpolation.
Keywords: Cayley Hamilton theorem, Interpolation polynomials, meromorphic function at a matrix
AMS Subject Classification:
Instructional exposition (textbooks; tutorial papers; etc.), , Canonical forms; reductions; classification, Interpolation
15-01, 15A16, 15A21, 41A05
PDF(click to download):
Interpolation Polynomials and Linear Algebra