Wilkinson matrix

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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[edit]

  1. ^ Wilkinson (1965). The Algebraic Eigenvalue Problem. Oxford University Press. ISBN 0-19-853418-3.