Triangular matrix: Difference between revisions

Revision as of 22:28, 10 October 2022

Revision as of 09:42, 28 November 2022

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{{for|the rings|triangular matrix ring}}

In the [[mathematics|mathematical]] discipline of [[linear algebra]], a '''triangular matrix''' is a special kind of [[square matrix]]. A square matrix is called '''{{visible anchor|lower triangular}}''' if all the entries ''above'' the [[main diagonal]] are zero. Similarly, a square matrix is called '''{{visible anchor|upper triangular}}''' if all the entries ''below'' the [[main diagonal]] are zero.

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'' and an upper triangular matrix ''U'' [[if and only if]] all its leading principal [[minor (linear algebra)|minors]] are non-zero.