English

Confluent Vandermonde matrix and related topics

Combinatorics 2025-08-26 v3

Abstract

In this note, we explore the connections between the confluent Vandermonde matrix over an arbitrary field and several mathematical topics, including interpolation polynomials, Hasse derivatives, LU factorization, companion matrices and their Jordan forms, and the partial fraction decomposition. Using a unified approach based on polynomial evaluations and derivative computations at selected points, we provide accessible proofs that not only clarify key results but also offer insights for both experienced researchers and those new to the subject.

Keywords

Cite

@article{arxiv.2403.01474,
  title  = {Confluent Vandermonde matrix and related topics},
  author = {Chi-Kwong Li and Jephian C. -H. Lin},
  journal= {arXiv preprint arXiv:2403.01474},
  year   = {2025}
}
R2 v1 2026-06-28T15:07:30.415Z