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A matrix which is simultaneously upper and lower triangular is [[diagonal matrix|diagonal]]. The [[identity matrix]] is the only matrix which is both normed upper and lower triangular.
A matrix which is simultaneously triangular and [[normal matrix|normal]], is also diagonal. This can be seen by looking at the diagonal entries of ''A''<sup>*</sup>''A'' and ''AA''<sup>*</sup>, where ''A'' is a normal, triangular matrix.
The [[transpose]] of a upper triangular matrix is a lower triangular matrix and vice versa. The [[determinant]] of a triangular matrix equals the product of the diagonal entries.
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.
Generally, operations can be performed on triangular matrices within half of the time that is needed for the same operation on a general matrix.
==Generalizations==
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