Kronecker delta Guide, Meaning , Facts, Information and Description

In mathematics, the Kronecker delta or Kronecker's delta, named after Leopold Kronecker (1823-1891), is a function of two variables, which is 1 if they are equal, and 0 otherwise. It is written as the symbol δ_ij, and treated as a notational shorthand rather than a function.

It has a remarkable property, which makes it a discrete analogue of the Dirac delta function. For :

which is similar to one of the main properties of the Dirac's delta:

The Kroenecker delta is used in many areas of mathematics. For example, in linear algebra, the identity matrix can be written as:

( δ_{i j} )

If it is considered as a tensor, the Kronecker tensor, it can be written

δ^j_i

with a contravariant index j. This is a more accurate way to notate the identity matrix, considered as a linear mapping.

See also

• Levi-Civita symbol
• Dirac delta function
• Dirac measure

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