The Kronecker delta, written δi j (\delta_{i\,j} in LaTeX), is a function of two variables defined as:

  • δi i = 1
  • δi j = 0 (i ≠ j)

The Kronecker delta can be defined over any set, but is usually defined on the base field of some vector space. It is commonly used in linear algebra.

The Dirac delta function is similar in some respects to the Kronecker delta, but unary and less discrete.

Actually, the Kronecker delta function can be defined with its domain as any nonempty set, so long as its codomain is a ring (even though its range will be the set of 0 and 1). However, it is usually only used as described above.

For those of you whose consoles do not display backslash-escaped characters, the Kronecker delta is usually displayed as a small delta (the one that looks curvy and like a d, not the big triangle). If your browser supports HTML 4.0 in all of its glory, it should look like this: δ.

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