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In mathematics, the Kronecker delta or Kronecker's delta, named after Leopold Kronecker, is a function of two variables, usually just positive integers. The function is 1 if the variables are equal, and 0 otherwise: : where the Kronecker delta δ''ij'' is a piecewise function of variables ''i'' and ''j''. For example, δ1 2 = 0, whereas δ3 3 = 1. The Kronecker delta appears naturally in many areas of mathematics, physics and engineering, as a means of compactly expressing its definition above. In linear algebra, the ''n'' × ''n'' identity matrix ''I'' has entries equal to the Kronecker delta: : where ''i'' and ''j'' take the values 1, 2, ..., ''n'', and the inner product of vectors can be written as : The restriction to positive integers is common, but there is no reason it cannot have negative integers as well as positive, or any discrete rational numbers. If ''i'' and ''j'' above take rational values, then for example δ−1, −3 = 0 and δ+1/2, −3/2 = 0 but δ−2,−2 = 1 and δ5/3, 5/3 = 1. This latter case is ultimately for convenience. == Properties == The following equations are satisfied: : Therefore, δ can be considered as an identity matrix. 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「Kronecker delta」の詳細全文を読む スポンサード リンク
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