# triangular matrix

(redirected from Upper-triangular)

## 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 ?
In the single-vector case, to prove [34, Lemma 6.1], expressions are derived for the inverses of upper-triangular matrices.
Table 1 shows the results of the average value of diagonal elements and upper-triangular for comparison of Rsk, Rkk, [R.sub.sh], and [R.sub.hh] in three different cases.
Branching rules in the ring of superclass functions of unipotent upper-triangular matrices.
Note that any poset J admits an upper-triangular numbering J = {[a.sub.1], ..., [a.sub.m]}; that is, [a.sub.i] [less than or equal to] [a.sub.j] implies i [less than or equal to] j.
To overcome these drawbacks, in this paper we propose an operational Galerkin strategy for solving Abel-Hammerstein integral equations of the second kind which applies Muntz-Legendre polynomials as natural basis functions to discretize the problem and to obtain a sparse nonlinear system with upper-triangular structure that can be solved directly.
Denote by [G.sub.n]([F.sub.q]), the group of n by n upper-triangular matrices over the field [F.sub.q] having q elements, and let [g.sub.n]([F.sub.q]) = Lie([G.sub.n]([F.sub.q])) denote the corresponding Lie algebra of n by n upper-triangular nilpotent matrices over [F.sub.q].
The new system is essentially dense in the upper-triangular part and appears to require O([n.sup.2]) storage.
In more detail, the group [UT.sub.n](q) acts on both sides of the algebra of strictly upper-triangular matrices [n.sub.n] (which can be thought of as [n.sub.n] = [UT.sub.n](q) - 1).
This is done by SCPRE that can generate a block diagonal preconditioner or a block upper-triangular one.
In this paper, we instead use an encoding of interval orders by upper-triangular matrices without zero rows and zero columns (we call such matrices Fishburn matrices.
Let the m-th hook sum of an upper-triangular matrix A = [[a.sub.i,j]] i[less than or equal to]i[less than or equal to]j[less than or equal to]n be given by
BGS with partitioning 3 is also the winner in the WebGoogle matrix with lower--triangular orientation for [alpha] [member of] {0.85,0.9} and upper-triangular orientation for a G {0.95,0.97,0.99}.

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