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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.

Synonyms

  • Identity
  • Identity Element

Hypernyms

  • Operator
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