Definition:Invariant

Definition

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

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Also see

• Definition:Invariant Theory

• 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