View source for Wilkinson matrix

{{Short description|Numerical lineral algebra}}
{{One source|date=August 2021}}
In [[linear algebra]], '''Wilkinson matrices''' are [[symmetric matrix|symmetric]], [[tridiagonal matrix|tridiagonal]], order-''N'' [[matrix (mathematics)|matrices]] with pairs of nearly, but not exactly, equal [[eigenvalue]]s.<ref>{{cite book | title = The Algebraic Eigenvalue Problem | author = Wilkinson | publisher = [[Oxford University Press]] | year = 1965 | isbn = 0-19-853418-3}}</ref> It is named after the British mathematician [[James H. Wilkinson]]. For ''N''&nbsp;=&nbsp;7, the Wilkinson matrix is given by

:<math>\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}.</math>

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

==References==
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{{Numerical linear algebra}}

[[Category:Matrices]]
[[Category:Numerical linear algebra]]


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