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An ''N''×''N'' Euclidean random matrix  is defined with the help of an arbitrary deterministic function ''f''(r, r′) and of ''N'' points randomly distributed in a region ''V'' of ''d''-dimensional Euclidean space. The element Aij of the matrix is equal to ''f''(ri, rj): Aij = ''f''(ri, rj). == History == Euclidean random matrices were first introduced in 1999. They studied a special case of functions ''f'' that depend only on the distances between the pairs of points: ''f''(r, r′) = ''f''(r - r′) and imposed an additional condition on the diagonal elements Aii, :Aij = ''f''(ri - rj) - u δij∑k''f''(ri - rk), motivated by the physical context in which they studied the matrix. A Euclidean distance matrix is a particular example of Euclidean random matrix with either ''f''(ri - rj) = |ri - rj|2 or ''f''(ri - rj) = |ri - rj|. 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「Euclidean random matrix」の詳細全文を読む スポンサード リンク
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