In linear algebra, Wilkinson matrices are symmetric, tridiagonal, order-N matrices with pairs of nearly, but not exactly, equal eigenvalues.[1] It is named after the British mathematician James H. Wilkinson. For N = 7, the Wilkinson matrix is given by
\begin{bmatrix} 3&1&0&0&0&0&0\\ 1&2&1&0&0&0&0\\ 0&1&1&1&0&0&0\\ 0&0&1&0&1&0&0\\ 0&0&0&1&1&1&0\\ 0&0&0&0&1&2&1\\ 0&0&0&0&0&1&3\\ \end{bmatrix}.
Wilkinson matrices have applications in many fields, including scientific computing, numerical linear algebra, and signal processing.