Eigenvalues and eigenvectors of symmetric centrosymmetric matrices

A. Cantoni, P. Butler

Research output: Contribution to journalArticle

222 Citations (Scopus)

Abstract

It is proved that the eigenvectors of a symmetric centrosymmetric matrix of order N are either symmetric or skew symmetric, and that there are ⌈N/2⌉ symmetric and ⌊N/2⌋ skew symmetric eigenvectors. Some previously known but widely scattered facts about symmetric centrosymmetric matrices are presented for completeness. Special cases are considered, in particular tridiagonal matrices of both odd and even order, for which it is shown that the eigenvectors corresponding to the eigenvalues arranged in descending order are alternately symmetric and skew symmetric provided the eigenvalues are distinct.

Original languageEnglish
Pages (from-to)275-288
Number of pages14
JournalLinear Algebra and Its Applications
Volume13
Issue number3
DOIs
Publication statusPublished - 1 Jan 1976
Externally publishedYes

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Centrosymmetric Matrix
Eigenvalues and Eigenvectors
Symmetric matrix
Eigenvalues and eigenfunctions
Skew
Eigenvector
Eigenvalue
Tridiagonal matrix
Completeness
Odd
Distinct

Cite this

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Eigenvalues and eigenvectors of symmetric centrosymmetric matrices. / Cantoni, A.; Butler, P.

In: Linear Algebra and Its Applications, Vol. 13, No. 3, 01.01.1976, p. 275-288.

Research output: Contribution to journalArticle

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