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Normal form
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Normal form

The term normal form is used in a variety of contexts. Many of the uses in mathematics are special cases of a single situation, looked at abstractly: within an equivalence class one specifies a representative element, which is in a simplest or most manageable or otherwise tidiest and most desirable form, in terms of structure or syntax. A little more loosely, an equivalence class might contain several examples of such special, distinguished elements. For example, the Jordan normal form under similarity of matrices (link below) may mean any suitable block matrix in similarity class, and in the general case there can be several such.

In Boolean algebra:

In Computation Theory and Languages: In relational database theory see database normalization for all four.

In linear algebra:

In musical set theory: To transform something into a normal form is often called normalization.

See also: canonical form