Triangular matrix: Difference between revisions

Revision as of 07:51, 14 April 2014

Revision as of 16:25, 24 May 2014

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In the [[mathematics|mathematical]] discipline of [[linear algebra]], a '''triangular matrix''' is a special kind of [[square matrix|square]] [[matrix (mathematics)|matrix]]. A square matrix is called '''lower triangular''' if all the entries ''above'' the [[main diagonal]] are zero. Similarly, a square matrix is called '''upper triangular''' if all the entries ''below'' the [[main diagonal]] are zero. A triangular matrix is one that is either lower triangular or upper triangular. A matrix that is both upper and lower triangular is called a [[diagonal matrix]].

Because matrix equations with triangular matrices are easier to solve, they are very important in [[numerical analysis]]. By the [[LU decomposition]] algorithm, an [[invertible matrix]] may be written as the product of a lower triangular matrix ''L'' byand an upper triangular matrix ''U'' [[if and only if]] all its leading principal [[minor (linear algebra)|minors]] are non-zero.

== Description ==