|
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 : for all ''i'', ''j''.〔. See page 193.〕 For example, 5-by-5 persymmetric matrices are of the form : 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）』 ■ウィキペディアで「Persymmetric matrix」の詳細全文を読む スポンサード リンク
|