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| | In [[linear algebra]], '''Wilkinson matrices''' are [[Symmetric matrix|symmetric]], [[Tridiagonal matrix|tridiagonal]], order-''N'' [[matrix (math)|matrices]] with pairs of nearly, but not exactly, equal [[eigenvalue]]s.<ref>{{cite book | title = The Algebraic Eigenvalue Problem | author = Wilkinson | edition = | publisher = [[Oxford University Press]] | year = 1965 | isbn = 0-19-853418-3}}</ref> It is named after the British mathematician [[James H. Wilkinson]]. For ''N'' = 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== |
| | {{reflist}} |
| | |
| | {{Numerical linear algebra}} |
| | |
| | [[Category:Matrices]] |
| | [[Category:Numerical linear algebra]] |
| | |
| | |
| | {{Linear-algebra-stub}} |
Revision as of 20:09, 28 January 2014
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
Wilkinson matrices have applications in many fields, including scientific computing, numerical linear algebra, and signal processing.
References
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Template:Numerical linear algebra
Template:Linear-algebra-stub
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