While the words operator and function are often used as synonyms, it is customary in some branches of mathematics to use the word operator in place of mapping, function or transformation. In particular, in linear algebra a transformation $T: V \to W$ is referred to as an operator on $V$ if $W = V$ . In general, in the branches of Algebra and Functional Analysis the term operator is preferred for transformations whose codomain is a subset of its domain.