Triangular matrix: Difference between revisions

Revision as of 11:22, 15 August 2004

Revision as of 14:15, 15 August 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.

Because matrix equations with triangular matrices are easy to calculatesolve they are very important in [[numerical analysis]]. The [[LU decomposition]] gives an algorithm to decompose any [[invertible matrix]] ''A'' into a normed upperlower triangle matrix ''L'' and aan normed lowerupper triangle matrix ''RU''.

== Definition ==

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A matrix equation with a normed upper triangular matrix ''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''.

== See also ==