Integrability of diagonalizable matrices and a dual Schoenberg type inequality

S. V. Danielyan, A. E. Guterman, T. W. Ng

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


The concepts of differentiation and integration for matrices were introduced for studying zeros and critical points of complex polynomials. Any matrix is differentiable, however not all matrices are integrable. The purpose of this paper is to investigate the integrability property and characterize it within the class of diagonalizable matrices. In order to do this we study the relation between the spectrum of a diagonalizable matrix and its integrability and the diagonalizability of the integral. Finally, we apply our results to obtain a dual Schoenberg type inequality relating zeros of polynomials with their critical points.

Original languageEnglish
Article number124909
JournalJournal of Mathematical Analysis and Applications
Issue number2
StatePublished - 15 Jun 2021
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2021 Elsevier Inc.


  • Differentiators
  • Integrators
  • Matrices
  • Non-derogatory
  • Polynomials


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