Identity Operator (Noun)
Meaning
An operator that leaves unchanged the element on which it operates; "the identity under numerical multiplication is 1".
Classification
Nouns denoting relations between people or things or ideas.
Examples
- The identity operator in matrix multiplication is the identity matrix.
- In group theory, the identity operator is denoted by e and it maps every element to itself.
- When applied to any set, the identity operator leaves all elements of the set unchanged.
- In algebra, the identity operator for addition is often denoted by 0, which, when added to any element, leaves the element unchanged.
- The identity operator in function composition is the function that maps every element to itself, effectively leaving the original input unchanged.