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Unitriangular matrix

If the entries on the main diagonal of a (upper or lower) triangular matrix are all 1, the matrix is called (upper or lower) unitriangular.

Other names used for these matrices are unit (upper or lower) triangular, or very rarely normed (upper or lower) triangular. However, a unit triangular matrix is not the same as the unit matrix, and a normed triangular matrix has nothing to do with the notion of matrix norm.

All finite unitriangular matrices are unipotent.