<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>This paper aims to show how some standard general results can be used to uncover the spectral theory of tridiagonal and related matrices more elegantly and simply than existing approaches. As a typical example, we apply the theory to the special tridiagonal matrices in recent papers on orthogonal polynomials arising from Jordan blocks. Consequently, we find that the polynomials and spectral theory of the special matrices are expressible in terms of the Chebyshev polynomials of second kind, whose properties yield interesting results. For special cases, we obtain results in terms of the Fibonacci numbers and Legendre polynomials.</p>
</abstract>

This paper aims to show how some standard general results can be used to uncover the spectral theory of tridiagonal and related matrices more elegantly and simply than existing approaches. As a typical example, we apply the theory to the special tridiagonal matrices in recent papers on orthogonal polynomials arising from Jordan blocks. Consequently, we find that the polynomials and spectral theory of the special matrices are expressible in terms of the Chebyshev polynomials of second kind, whose properties yield interesting results. For special cases, we obtain results in terms of the Fibonacci numbers and Legendre polynomials.

On tridiagonal matrices associated with Jordan blocks

Doha District, Safat 13133, Kuwait and Chair of Computational Mathematics, University of Deusto

Acta Universitatis Sapientiae, Mathematica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"On tridiagonal matrices associated with Jordan blocks"}

This paper aims to show how some standard general results can be used to uncover the spectral theory of tridiagonal and related matrices more elegantly and...

On tridiagonal matrices associated with Jordan blocks

Publicado en línea: 18 nov 2022

Páginas: 61 - 74

Recibido: 01 mar 2021

DOI: https://doi.org/10.2478/ausm-2022-0004

Palabras clave
tridiagonal matrices, characteristic polynomial, eigenvalues, Chebyshev polynomials of the second kind, Jordan blocks

© 2022 Carlos M. da Fonseca et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

On tridiagonal matrices associated with Jordan blocks

Publicado en línea: 18 nov 2022

Páginas: 61 - 74

Recibido: 01 mar 2021

DOI: https://doi.org/10.2478/ausm-2022-0004

Palabras clavetridiagonal matrices, characteristic polynomial, eigenvalues, Chebyshev polynomials of the second kind, Jordan blocks

© 2022 Carlos M. da Fonseca et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Palabras clave
tridiagonal matrices, characteristic polynomial, eigenvalues, Chebyshev polynomials of the second kind, Jordan blocks