Low rank perturbations and the spectrum of a tridiagonal sign pattern

✍ Scribed by L. Elsner; D.D. Olesky; P. van den Driessche

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 125 KB
• Volume: 374
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/s0024-3795(03)00580-9

✦ Synopsis

The n-by-n tridiagonal sign pattern T n has every superdiagonal entry positive, every subdiagonal entry negative, the (1, 1) entry negative, the (n, n) entry positive and every other diagonal entry zero. Inertia and spectral results for matrices A n having the sign pattern T n are proved using new techniques on low rank perturbations. It is also shown (by using MAPLE) that for 8 n 16, T n allows any spectrum. These results extend those previously in the literature, and strengthen the conjecture that T n allows any spectrum for all values of n. In addition, bounds on the algebraic multiplicity of an eigenvalue of a low rank perturbation of a general matrix are obtained.