triangular matrix

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

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

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

Since is a triangular matrix, its eigenvalues are obviously .

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

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

These use a triangular matrix of pairwise language comparisons.

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

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

The lower triangular matrix with strictly positive diagonal entries is invertible.

Jordan blocks commute with upper triangular matrices that have the same value along bands.

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

The analogous result holds for lower triangular matrices.

The result is the upper triangular matrix R1.

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

Their Lie algebras consist of upper and lower strictly triangular matrices.

Thus, in the above example, Another useful property of triangular matrices is the ease with which their reciprocals may be calculated.

The matrix and its inverse are triangular matrices.

Denote the upper triangular matrix A by U, and .

Likewise, inverses of triangular matrices are algorithmically easier to calculate.

Here is a square right triangular matrix, and the zero matrix has dimension .

The analogous results hold for lower triangular matrices, so they also form a Lie subalgebra.

The Moebius transformations fixing are just the upper triangular matrices.

We have already seen, in that reciprocation of a triangular matrix can be achieved by a simple process of back-substitution.

For example, a real triangular matrix has its eigenvalues along its diagonal, but in general is not symmetric.