Kronecker delta: Difference between revisions
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In [[algebra]], the '''Kronecker delta''' is a notation <math>\delta_{ij}</math> for a quantity depending on two subscripts ''i'' and ''j'' which is equal to one when ''i'' and ''j'' are equal and zero when they are unequal. | {{subpages}} | ||
In [[algebra]], the '''Kronecker delta''' is a notation <math>\delta_{ij}</math> for a quantity depending on two subscripts ''i'' and ''j'' which is equal to one when ''i'' and ''j'' are equal and zero when they are unequal: | |||
:<math> | |||
\delta_{ij} = | |||
\begin{cases} | |||
1 &\quad\mathrm{if} \quad i = j \\ | |||
0 &\quad\mathrm{if} \quad i \ne j. | |||
\end{cases} | |||
</math> | |||
If the subscripts are taken to vary from 1 to ''n'' then δ gives the entries of the ''n''-by-''n'' [[identity matrix]]. The invariance of this matrix under [[orthogonal matrix|orthogonal]] change of coordinate makes δ a rank two [[tensor]]. | If the subscripts are taken to vary from 1 to ''n'' then δ gives the entries of the ''n''-by-''n'' [[identity matrix]]. The invariance of this matrix under [[orthogonal matrix|orthogonal]] change of coordinate makes δ a rank two [[tensor]]. | ||
Revision as of 08:50, 20 December 2008
In algebra, the Kronecker delta is a notation for a quantity depending on two subscripts i and j which is equal to one when i and j are equal and zero when they are unequal:
If the subscripts are taken to vary from 1 to n then δ gives the entries of the n-by-n identity matrix. The invariance of this matrix under orthogonal change of coordinate makes δ a rank two tensor.