# triangular matrix

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## triangular matrix

[trī′aŋ·gyə·lər ′mā·triks]
(mathematics)
A matrix where either all entries above or all entries below the principal diagonal are zero.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
A square NSM A = [[[a.sub.ij]].sub.n x n] is called upper triangular NSM if [a.sub.ij] = (0,1,1), [for all]i > j and is called lower triangular NSM if [a.sub.ij] = (0,1,1), [for all]i < j.
(3) Because the system is an underactuated system which is not the quasi lower triangular structure, one cannot use the design method of vector controller in [9-12].
where L is a lower triangular matrix and Q is a unitary matrix.
The upper branch passed along the base of axilla, then left the axilla by passing through lower triangular space and finally joined with posterior cutaneous nerve of arm on each side whereas the lower branch passed along the base of axilla to reach the upper and medial part of arm where they join with medial cutaneous nerve of arm on each side.
In the triangular settler, some of the channels were totally blocked because the sludge was stuck in the lower triangular section, which results in clogging of entire channels or in heavy sludge deposit in the acute angles of the triangular channels.
with [L.sub.11] being the lower triangular matrix in the LU triangular decomposition of [A.sub.11].
We can show that the lower triangular matrix in the classical Cholesky decomposition can be obtained by the QR factorization and vice versa.
Where L [member of] [R.sup.nxn] is a lower triangular matrix and U [member of] [R.sup.nxn] is upper triangular, as follows: first solve Lb'= b by forward substitution, and then solve Ux = b' by backward substitution to obtain the solution .
LU-Factorization [16] is based on the fact that it is a matrix decomposition and nonsingular square matrix 'A' can be replaced as the product of lower triangular and upper triangular matrices.
al.[14] used a method to reduce the number of computations while quadratic term calculation by representing the same as a monotonically increasing sum of squares by using the methods--Unitary and Lower Triangular canonical forms (UCF and LTCF).

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