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

$\left[\begin{array}{ccccccc}3& 1& 0& 0& 0& 0& 0\\ 1& 2& 1& 0& 0& 0& 0\\ 0& 1& 1& 1& 0& 0& 0\\ 0& 0& 1& 0& 1& 0& 0\\ 0& 0& 0& 1& 1& 1& 0\\ 0& 0& 0& 0& 1& 2& 1\\ 0& 0& 0& 0& 0& 1& 3\end{array}\right].$

Wilkinson matrices have applications in many fields, including scientific computing, numerical linear algebra, and signal processing.