triangular matrix

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triangular matrix A square matrix in which every element lying to one side of the main diagonal is equal to zero. Thus for a lower triangular matrix, L, lij = 0 if i < j

and for an upper triangular matrix, U, uij = 0 if i > j

If, in addition, lii = 0 or uii = 0

then L or U is said to be strictly lower or strictly upper triangular respectively. The inverse of a lower (or an upper) triangular matrix, if it exists, is easy to calculate and is itself lower (or upper) triangular.

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triangular matrix

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