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In mathematics, especially in linear algebra and matrix theory, a centrosymmetric matrix is a matrix which is symmetric about its center. More precisely, an ''n'' × ''n'' matrix ''A'' = (''A''i,j ) is centrosymmetric when its entries satisfy :''A''i,j = ''A''n−i+1,n−j+1 for 1 ≤ i,j ≤ n. If ''J'' denotes the ''n'' × ''n'' matrix with 1 on the counterdiagonal and 0 elsewhere (that is, ''J''i,n+1-i = 1; ''J''i,j = 0 if j ≠ n+1-i), then a matrix ''A'' is centrosymmetric if and only if ''AJ = JA''. The matrix ''J'' is sometimes referred to as the exchange matrix. ==Examples== * All 2×2 centrosymmetric matrices have the form : * All 3×3 centrosymmetric matrices have the form : * Symmetric Toeplitz matrices are centrosymmetric. 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「Centrosymmetric matrix」の詳細全文を読む スポンサード リンク
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