1
$\begingroup$

I was wondering if there is a special name for the following kind of tridiagonal matrices ? And if yes, are there any books or articles which talk about their properties ?

\begin{pmatrix} \alpha_1 & \beta_1 & 0 & 0 \\ \beta_{n-1} & \alpha_2 & \ddots & 0 \\ 0 & \ddots & \ddots & \beta_{n-1} \\ 0 & 0 & \beta_1 & \alpha_n \end{pmatrix}

(basically the lower diagonal is reversed compared to the upper diagonal)

$\endgroup$

1 Answer 1

Reset to default
0
$\begingroup$

I was not able to find any specific literature on it, but the closest terminology I would have to describe what you proposed would be a "centrosymmetric tridiagonal matrix".

In page of the following document (p.5) you can find a similar matrix in Eq. (2.5) to what you are looking for: https://core.ac.uk/download/pdf/81151355.pdf

$\endgroup$
2
  • $\begingroup$ Nice! Thanks a lot :) That answers my question! $\endgroup$
    – Ivan R.
    Commented Apr 14, 2021 at 17:48
  • $\begingroup$ In order to be a "centrosymmetric tridiagonal matrix" the main diagonal would need to be *palindromic" (the same values if reversed from upper left to lower right). $\endgroup$
    – hardmath
    Commented Oct 14, 2023 at 2:23

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .