Editing Triangular matrix (section)

{{Short description|Special kind of square matrix}}
{{distinguish|text=a [[triangular array]], a related concept}}
{{for|the rings|triangular matrix ring}}{{Redirects here|Triangularization|the geometric process|Triangulation}}
In mathematics, 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 [[matrix multiplication|product]] of a lower triangular matrix ''L'' and an upper triangular matrix ''U'' [[if and only if]] all its leading principal [[minor (linear algebra)|minor]]s are non-zero.