Spectra of a class of non-self-adjoint matrices
| Autor: | Davies, E. Brian, Levitin, Michael |
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| Rok vydání: | 2013 |
| Předmět: | |
| Zdroj: | Linear Algebra and its Applications, Volume 448, Pages 55-84, 2014 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.laa.2014.01.025 |
| Popis: | We consider a new class of non-self-adjoint matrices that arise from an indefinite self-adjoint linear pencil of matrices, and obtain the spectral asymptotics of the spectra as the size of the matrices diverges to infinity. We prove that the spectrum is qualitatively different when a certain parameter $c$ equals $0$, and when it is non-zero, and that certain features of the spectrum depend on Diophantine properties of $c$. Comment: 32 pages, 8 figures; movie file frames3e.mp4, Mathematica 7 notebook makemovie.nb and its listing makemovie.pdf are available for download from Ancillary files section of the menu |
| Databáze: | arXiv |
| Externí odkaz: |
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