On the eigenvalues of double band matrices

✍ Scribed by Tyler McMillen

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 140 KB
• Volume: 431
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/j.laa.2009.06.026

✦ Synopsis

We consider matrices containing two diagonal bands of positive entries. We show that all eigenvalues of such matrices are of the form rζ , where r is a nonnegative real number and ζ is a pth root of unity, where p is the period of the matrix, which is computed from the distance between the bands. We also present a problem in the asymptotics of spectra in which such double band matrices are perturbed by banded matrices.