For the TSQR algorithm, though only one reduce is required throughout the algorithm, the reduction operation is a non-standard one, which corresponds to computing the QR decomposition of a 2nxn matrix formed by concatenating two upper triangular matrices
Let A = D - L-U, where D is the diagonal matrix and L, U are strictly lower and strictly upper triangular matrices
of A, respectively.
q]) denote the group of unipotent n x n upper triangular matrices
over the q element field [F.
In Section 2 we review the suggested algorithm for finding the inverse of the lower triangular matrices
3, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] are non-singular lower triangular matrices
with [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
Let 1 < k [less than or equal to] s < [infinity], A and B be doubly triangular matrices
with A satisfying
For FIML, identical results are obtained for the two equations and triangular matrices
Hausdorff matrices were shown by Hurwitz and Silverman  to be the class of triangular matrices
that commute with C, the Cesaro matrix of order one.
However, the author anticipates that obtaining the triangular matrices
will increase the complexity and information content thus decreasing the probability of success of completing the analysis.
Let ST(2) be the Lie group of upper triangular matrices
2x2 with determinant equal to 1 such that the operation of the group is the multiplication between matrices.
The hand-coded version considers the size of M and N and calls specialized routines from the BLAS library to compute the solve operation (\) and the matrix multiplication (N * x) for triangular matrices
Second, we develop efficiently implementable variants of guaranteed reliable RRQR algorithms for triangular matrices
originally suggested by Chandrasekaran and Ipsen and by Pan and Tang.