On polynomial Schur's matrix

Chih-Nung Hsu, Ting Ting Nan

Research output: Contribution to journalArticle

Abstract

Classical Schur's matrix is a different evaluation, provided by Schur, of the quadratic Gaussian sum from Gauss. The advanced information was studied by L. Carlitz who determined its eigenvalues, and by P. Morton who determined its eigenvectors. In this paper, we generalize the classical Schur's matrix to the case in polynomial rings over finite fields, and what is more, we give explicit formulas for the determinant, inverse matrix, eigenvalues, multiplicity and eigenvectors with respect to each eigenvalue of the polynomial Schur's matrix.

Original languageEnglish
Pages (from-to)652-660
Number of pages9
JournalFinite Fields and their Applications
Volume15
Issue number6
DOIs
Publication statusPublished - 2009 Dec 1

Fingerprint

Schur Polynomials
Polynomials
Eigenvalue
Eigenvector
Eigenvalues and eigenfunctions
Inverse matrix
Polynomial ring
Gauss
Galois field
Explicit Formula
Multiplicity
Determinant
Generalise
Evaluation

Keywords

  • Character sum
  • Eigenvectors
  • Polynomial ring

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Algebra and Number Theory
  • Engineering(all)
  • Applied Mathematics

Cite this

On polynomial Schur's matrix. / Hsu, Chih-Nung; Nan, Ting Ting.

In: Finite Fields and their Applications, Vol. 15, No. 6, 01.12.2009, p. 652-660.

Research output: Contribution to journalArticle

Hsu, Chih-Nung ; Nan, Ting Ting. / On polynomial Schur's matrix. In: Finite Fields and their Applications. 2009 ; Vol. 15, No. 6. pp. 652-660.
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