Upper triangular matrix
In mathematics, a triangular matrix is a matrix with entries that have elements either completely above (upper triangular) or completely below (lower triangular) the principal diagonal.
For example:
is upper triangular and
is lower triangular.
The product of two upper triangular matrices is upper triangular, so the set of upper triangular matrices forms an algebra. Algebras of upper triangular matrices have a natural generalisation in functional analysis which yields nest algebras.
See also: Row echelon form, LU decomposition
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