Math Writing Style: Use of the Term “Linear Operator” vs “Linear Function”

By Xah Lee. Date: 2013-10-02

here's a excerpt from Wikipedia Laplace transform

The Laplace transform is a widely used integral transform with many applications in physics and engineering. Denoted ℒ{f} (or alternatively ℒ{f[t]} ), it is a linear operator of a function f(t) with a real argument t (t ≥ 0) that transforms f(t) to a function F(s) with complex argument s.

mathematicans, can you stop using the term “operator” and use “function” instead? Because, you are not talking about syntax, you are talking about meaning.

the writing style, in the context of linguistics and certain sense of logic, the “operator” in “linear operator” means a symbol in math notation. It refers to syntax, namely, the symbol ℒ on paper.

the reason that people write “linear operator” instead of “linear function” is due to lose unspoken convention. This convention, came about, is probably because: it gives them something concrete to speak of, namely the symbol shown on paper.