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persymmetric matrix : ウィキペディア英語版
persymmetric matrix
In mathematics, persymmetric matrix may refer to:
# a square matrix which is symmetric in the northeast-to-southwest diagonal; or
# a square matrix such that the values on each line perpendicular to the main diagonal are the same for a given line.
The first definition is the most common in the recent literature. The designation "Hankel matrix" is often used for matrices satisfying the property in the second definition.
== Definition 1 ==

Let ''A'' = (''a''''ij'') be an ''n'' × ''n'' matrix. The first definition of ''persymmetric'' requires that
: a_ = a_ for all ''i'', ''j''.〔. See page 193.〕
For example, 5-by-5 persymmetric matrices are of the form
: A = \begin
a_ & a_ & a_ & a_ & a_ \\
a_ & a_ & a_ & a_ & a_ \\
a_ & a_ & a_ & a_ & a_ \\
a_ & a_ & a_ & a_ & a_ \\
a_ & a_ & a_ & a_ & a_
\end.
This can be equivalently expressed as ''AJ = JA''T where ''J'' is the exchange matrix.
A symmetric matrix is a matrix whose values are symmetric in the northwest-to-southeast diagonal. If a symmetric matrix is rotated by 90°, it becomes a persymmetric matrix. Symmetric persymmetric matrices are sometimes called bisymmetric matrices.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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