Wilkinson matrix

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.

References

^ Wilkinson (1965). The Algebraic Eigenvalue Problem. Oxford University Press. ISBN 0198534183.