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nest algebras reference |
QR decomposition, common notation, efficiency. |
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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 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.'
See also: [[Row echelon form]], [[LU decomposition]]▼
Generally, operations can be performed on triangular matrices within half the time.
▲See also: [[Row echelon form]], [[LU decomposition]], [[QR decomposition]]
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