# Definition:Invariant

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## Definition

An **invariant** is a property of an object which is retained under an isomorphism of some kind.

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## Also see

- Results about
**invariants**can be found**here**.

## Historical Note

**Invariants** were investigated by David Hilbert, who proved important general results about the set of all **algebraic invariants** of certain groups of transformations.

It is noted that the problem of calculation and full description of all possible **invariants** can be difficult, if not intractable.

## Linguistic Note

The property of being **invariant** is called **invariance**.

## Sources

- 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**invariant** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**invariant**