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In linear algebra, a nilpotent matrix is a square matrix ''N'' such that : for some positive integer ''k''. The smallest such ''k'' is sometimes called the degree or index of ''N''. More generally, a nilpotent transformation is a linear transformation ''L'' of a vector space such that ''L''''k'' = 0 for some positive integer ''k'' (and thus, ''L''''j'' = 0 for all ''j'' ≥ ''k''). Both of these concepts are special cases of a more general concept of nilpotence that applies to elements of rings. ==Examples== The matrix : is nilpotent, since ''M''2 = 0. More generally, any triangular matrix with 0s along the main diagonal is nilpotent. For example, the matrix : is nilpotent, with : Though the examples above have a large number of zero entries, a typical nilpotent matrix does not. For example, the matrix : squares to zero, though the matrix has no zero entries. 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「nilpotent matrix」の詳細全文を読む スポンサード リンク
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