Math 6610 • Analysis of Numerical Methods I

{A Matrix}
Compute the eigenvalues and eigenvectors of the tridiagonal \(N\times N\) matrix
\[
\setlength{\arraycolsep}{5pt}
  A=
  \begin{bmatrix}
    2 & 1 & 0 & \cdots & 0 & 0\\
    1 & 2 & 1 & \cdots & 0 & 0\\
    0 & 1 & 2 & \ddots & 0 & 0\\
    \vdots & \vdots & \ddots & \ddots & \ddots & \vdots\\
    0 & 0 & 0 & \ddots & 2 & 1\\
    0 & 0 & 0 & \cdots & 1 & 2
  \end{bmatrix}. \tag{2}
\]
Note that the diagonal entries are indeed meant to be positive 2, not -2.