triangular matrix

The final algorithm looks very much like an iterated product of triangular matrices.

The upper triangular matrices are precisely those that stabilize the standard flag.

This condition can be checked each time a new row k of the triangular matrix is obtained.

The divided difference scheme can be put into an upper triangular matrix.

Since is a triangular matrix, its eigenvalues are obviously .

Thus, for example are, respectively, lower and upper triangular matrices.

More generally, any triangular matrix with 0s along the main diagonal is nilpotent.

The group would be the upper triangular matrices with integral coefficients.

On the other hand the action on X is simple to define for lower triangular matrices.

In fact, this is also true for the subring of upper triangular matrices.