Triangular matrix: Difference between revisions

Revision as of 20:51, 18 July 2004

Revision as of 13:38, 19 July 2004

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In the [[mathematics | mathematical]] discipline of [[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 ==

A matrix ''L'' of the form

:<math> \mathbf{L}=

\begin{pmatrix}

l_{1,1} & & & & 0 \\

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</math>

which can be solved by the following rekursiverecursive relation

:<math>

\begin{matrix}

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:</math>

A matrix equation with a normed upper triangular matrix R''U'' can be solved in an analogous way.

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''.