Wilkinson matrix

In linear algebra, Wilkinson matrices are symmetric, tridiagonal, order-N matrices with pairs of nearly, but not exactly, equal eigenvalues. 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.