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

The result's identifiers

  • Result code in 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>

  • Result on the web

    <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>

Alternative languages

  • Result language

    angličtina

  • Original language name

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

  • Original language description

    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.

  • Czech name

  • Czech description

Classification

  • Type

    J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

  • CEP classification

    BA - General mathematics

  • OECD FORD branch

Result continuities

  • Project

    Result was created during the realization of more than one project. More information in the Projects tab.

  • Continuities

    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

Others

  • Publication year

    2011

  • Confidentiality

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

Data specific for result type

  • Name of the periodical

    Linear Algebra and Its Applications

  • ISSN

    0024-3795

  • e-ISSN

  • Volume of the periodical

    434

  • Issue of the periodical within the volume

    5

  • Country of publishing house

    US - UNITED STATES

  • Number of pages

    18

  • Pages from-to

    1336-1353

  • UT code for WoS article

    000286720700013

  • EID of the result in the Scopus database