Identity function

Graph of the identity function on the real numbers

In mathematics, an identity function, also called an identity relation, identity map or identity transformation, is a function that always returns the value that was used as its argument, unchanged. That is, when x to which X is a set, the identity function X as its domain and codomain, satisfying

f(x)=x</math> for all elements <math>x</math> in <math>X</math>.<ref>{{Cite book |last=Knapp |first=Anthony W. |title=Basic algebra |publisher=Springer |year=2006 |isbn=978-0-8176-3248-9}}</ref>"}},"i":0}}]}'>

In other words, the function value x in the domain f on X.

If ∘" denotes function composition. In particular, X (under function composition).

Since the identity element of a monoid is unique, one can alternately define the identity function on n-dimensional vector space the identity function is represented by the identity matrix

↑ Knapp, Anthony W. (2006). Basic algebra. Springer. ISBN 978-0-8176-3248-9.

↑ Nel, Louis (2016). Continuity Theory. Cham: Springer. p. 21. doi:10.1007/978-3-319-31159-3. ISBN 978-3-319-31159-3.

↑ T. S. Shores (2007). Applied Linear Algebra and Matrix Analysis. Undergraduate Texts in Mathematics. Springer. ISBN 978-038-733-195-9.

↑ Conover, Robert A. (2014-05-21). A First Course in Topology: An Introduction to Mathematical Thinking. Courier Corporation. p. 65. ISBN 978-0-486-78001-6.

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