Interpolation Polynomials and Linear Algebra

C. R. Math. Rep. Acad. Sci. Canada Vol. 44 (2) 2022, pp. 33-49
(Received: 2022-03-11 , Revised: 2022-04-05)

Askold Khovanskii, FRSC, University of Toronto, Toronto, Canada; e-mail:

Sushil Singla, Department of Mathematics, Shiv Nadar University, Greater Noida, India 201314; e-mail:

Aaron Tronsgard, University of Toronto, Toronto, Canada; e-mail:


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

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