Self-interlacing polynomials II: Matrices with self-interlacing spectrum
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2016
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866916813886980096 |
|---|---|
| author | Tyaglov, Mikhail |
| author_facet | Tyaglov, Mikhail |
| contents | An $n\times n$ matrix is said to have a self-interlacing spectrum if its eigenvalues $λ_k$, $k=1,\ldots,n$, are distributed as follows $$ λ_1>-λ_2>λ_3>\cdots>(-1)^{n-1}λ_n>0. $$
A method for constructing sign definite matrices with self-interlacing spectra from totally nonnegative ones is presented. We apply this method to bidiagonal and tridiagonal matrices. In particular, we generalize a result by O. Holtz on the spectrum of real symmetric anti-bidiagonal matrices with positive nonzero entries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1612_05102 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | Self-interlacing polynomials II: Matrices with self-interlacing spectrum Tyaglov, Mikhail Classical Analysis and ODEs Spectral Theory 15A18, 15B05, 12D10, 15B35, 15B48 An $n\times n$ matrix is said to have a self-interlacing spectrum if its eigenvalues $λ_k$, $k=1,\ldots,n$, are distributed as follows $$ λ_1>-λ_2>λ_3>\cdots>(-1)^{n-1}λ_n>0. $$ A method for constructing sign definite matrices with self-interlacing spectra from totally nonnegative ones is presented. We apply this method to bidiagonal and tridiagonal matrices. In particular, we generalize a result by O. Holtz on the spectrum of real symmetric anti-bidiagonal matrices with positive nonzero entries. |
| title | Self-interlacing polynomials II: Matrices with self-interlacing spectrum |
| topic | Classical Analysis and ODEs Spectral Theory 15A18, 15B05, 12D10, 15B35, 15B48 |
| url | https://arxiv.org/abs/1612.05102 |