PlanetMath: Hessenberg matrix

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Hessenberg matrix

(Definition)

An upper Hessenberg matrix is of the form

$\displaystyle \begin{bmatrix} a_{11} & a_{12} & a_{13} & \cdots & a_{1,n-1} & a... ... \ddots & \vdots & \vdots \ 0 & 0 & 0 & 0 & a_{n,n-1} & a_{nn} \end{bmatrix}$

and a lower Hessenberg matrix is of the form

$\displaystyle \begin{bmatrix} a_{11} & a_{12} & 0 & \cdots & 0 & 0 \ a_{21} &... ...} \ a_{n,1} & a_{n,2} & a_{n,3} & \cdots & a_{n,n-1} & a_{n,n} \end{bmatrix}$

"Hessenberg matrix" is owned by akrowne.

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Other names:

upper Hessenberg matrix, lower Hessenberg matrix, upper Hessenberg, lower Hessenberg

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This is version 2 of Hessenberg matrix, born on 2002-01-14, modified 2006-10-28.
Object id is 1475, canonical name is HessenbergMatrix.
Accessed 11912 times total.

Classification:

AMS MSC:	15-00 (Linear and multilinear algebra; matrix theory :: General reference works )
	65-00 (Numerical analysis :: General reference works )

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