# Eigen Values for a standard form of tridiagonal Matrices

In my attempt to find a formal solution to a problem in Chemical physics, I have come across a matrix of this form:

$$\begin{bmatrix} 0 & V_{12} & 0 & \cdots & \cdots &0 \\ V_{21} & 0 & V_{23} & \cdots & \cdots &0 \\ 0 & V_{32} & 0 & \ddots & &\vdots \\ \vdots & \vdots & \ddots & \ddots &\ddots &\vdots \\ \vdots & \vdots & & \ddots &\ddots & V_{_{(N-1)N}} \\ 0 & 0 & \cdots &\cdots &V_{N(N-1)} & 0 \\ \end{bmatrix}$$

where $$V_{ij} = \cos(\theta_i - \theta_j)$$

• It does not look that restriction $V_{ij} = \cos(\theta_i - \theta_j)$ is of any use (assuming $\theta_i$ being arbitrary) comparing with $V_{ij}=V_{ji}$. Besides you forgot to formulate a question in the body of your text (from the title I guess you are interested in computing the eigenvalues of the matrix). – user Jan 12 at 11:25
• Is there any relation between $\theta$s? – user376343 Feb 5 at 21:02
• No there is no explicit relation between $\theta's$ – EverydayFoolish Feb 6 at 7:34