On the eigenvalue problem for a particular class of finite Jacobi matrices

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F11%3A00173575" target="_blank" >RIV/68407700:21340/11:00173575 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.laa.2010.11.010" target="_blank" >http://dx.doi.org/10.1016/j.laa.2010.11.010</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.laa.2010.11.010" target="_blank" >10.1016/j.laa.2010.11.010</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On the eigenvalue problem for a particular class of finite Jacobi matrices

Popis výsledku v původním jazyce

A function F with simple and nice algebraic properties is defined on a subset of the space of complex sequences. Some special functions are expressible in terms of F, first of all the Bessel functions of first kind. A compact formula in terms of the function F is given for the determinant of a Jacobi matrix. Further we focus on the particular class of Jacobi matrices of odd dimension whose parallels to the diagonal are constant and whose diagonal depends linearly on the index. A formula is derived for the characteristic function. Yet another formula is presented in which the characteristic function is expressed in terms of the function F in a simple and compact manner. A special basis is constructed in which the Jacobi matrix becomes a sum of a diagonal matrix and a rank-one matrix operator. A vector-valued function on the complex plain is constructed having the property that its values on spectral points of the Jacobi matrix are equal to corresponding eigenvectors.

Název v anglickém jazyce

On the eigenvalue problem for a particular class of finite Jacobi matrices

Popis výsledku anglicky

A function F with simple and nice algebraic properties is defined on a subset of the space of complex sequences. Some special functions are expressible in terms of F, first of all the Bessel functions of first kind. A compact formula in terms of the function F is given for the determinant of a Jacobi matrix. Further we focus on the particular class of Jacobi matrices of odd dimension whose parallels to the diagonal are constant and whose diagonal depends linearly on the index. A formula is derived for the characteristic function. Yet another formula is presented in which the characteristic function is expressed in terms of the function F in a simple and compact manner. A special basis is constructed in which the Jacobi matrix becomes a sum of a diagonal matrix and a rank-one matrix operator. A vector-valued function on the complex plain is constructed having the property that its values on spectral points of the Jacobi matrix are equal to corresponding eigenvectors.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)<br>S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2011

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Linear Algebra and Its Applications

ISSN

0024-3795

e-ISSN

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Svazek periodika

434

Číslo periodika v rámci svazku

5

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

18

Strana od-do

1336-1353

Kód UT WoS článku

000286720700013

EID výsledku v databázi Scopus

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