# 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 ?
where [??] is the following infinite upper-triangular matrix
and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is an infinite upper-triangular matrix with nonzero entries
where the infinite upper-triangular matrix [??] is obtained from (3.11) with [k.sub.j,l-j] in place of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
In this case, [C.sub.J] [member of] [M.sub.m](Z) is an upper-triangular matrix with 1 on the main diagonal, and, hence, det [C.sub.J] = 1, and det [C.sub.J'] = 1, for any numbering J' = {[a'.sub.1], ..., [a'.sub.m]}.
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
Equivalently, if an upper-triangular matrix has only the nonzero entries [g.sub.[pi]](i) at (i, [h.sub.[pi]](i)), then it is a Tesler matrix.
If an upper-triangular matrix has only the nonzero entries [g.sub.[pi]](i) at (i, [h.sub.[pi]](i)), then the i-th hook sum is [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
The back substitution, in both methods, involves an upper-triangular matrix with a definite rank structure.
It has become clear in recent years that the representation theory finite group of unipotent upper-triangular matrix groups Un(q) can lead to a similarly rich combinatorial theory.
An upper-triangular matrix T was constructed as follows.
We computed the eigenvalues of H and [??] by the QR algorithm and checked their accuracy by comparing them with the eigenvalues of the original upper-triangular matrix T.

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