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The product of two upper triangular matrices is upper triangular, so the set of upper triangular matrices forms an [[associative algebra|algebra]]. Algebras of upper triangular matrices have a natural generalisation in [[functional analysis]] which yields [[nest algebra]]s.
The [[transpose]] of a upper triangular matrix is a lower triangular matrix and vice versa.
The variable L is commonly used for lower triangular matrix, standing for lower/left, while the variable U or R is commonly used for upper triangular matrix, standing for upper/right. The variable R has the added benefit of being the same initial for the German term for 'right.'
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