Complex wedge-shaped matrices: A generalization of Jacobi matrices

• ID: 2707, RIV: 10315161
• ISSN: 0024-3795, ISBN: not specified
• source: Linear Algebra and Its Applications
• keywords: Eigenvalues; Eigenvectors; Wedge-shaped matrices; Generalized Jacobi matrices; Band (or block) Krylov subspace methods
• authors: Iveta Hnětynková, Martin Plesinger
• authors from KNM: Hnětynková Iveta

Abstract

The paper by I. Hnetynkova et al. (2015) [11] introduces real wedge-shaped matrices that can be seen as a generalization of Jacobi matrices, and investigates their basic properties. They are used in the analysis of the behavior of a Krylov subspace method: The band (or block) generalization of the Golub-Kahan bidiagonalization. Wedge-shaped matrices can be linked also to the band (or block) Lanczos method. In this paper, we introduce a complex generalization of wedge-shaped matrices and show some further spectral properties, complementing the already known ones. We focus in particular on nonzero components of eigenvectors.