Triangular matrix: Difference between revisions

Revision as of 15:35, 29 June 2004

Revision as of 18:04, 18 July 2004

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[[es:Matriz triangular]]

[[ja:三角行列]]

[[Category:Linear algebra]]

[[Category:Matrix theory]]

[[Category:Numerical analysis]]

In [[linear algebra]], a '''triangular matrix''' is a special kind of [[Matrix_(mathematics)|matrix]] where the entries below or above the [[main diagonal]] are zero.

== Definition ==

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</math>

the matrix is called '''unit upper triangular matrix''' or '''normed upper triangular matrix'''.

== Notes ==

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Generally, operations can be performed on triangular matrices within half the time.

== Examples ==

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\end{pmatrix}</math>

is lower triangular.

== Application ==

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Because triangular matrices are easy to calculate they are very important in numerical analysis.The [[LU decomposition]] gives an algorithm to decompose any [[invertible matrix]] ''A'' into a normed upper triangle matrix ''L'' and a normed lower triangle matrix ''R''.

== See also ==

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* [[QR decomposition]]

* [[Hessenberg matrix]]

[[es:Matriz triangular]]

[[ja:&#19977;&#35282;&#34892;&#21015;]]

[[Category:Linear algebra]]

[[Category:Matrix theory]]

[[Category:Numerical analysis]]