operator

Operator

A (usually unary) transformation $T$ between or often within spaces:

$$T:X\to Y$$

Examples

derivatives on the space of differentiable functions: $T(f)=\frac{df}{dx}$
linear transformations: $T(\mathbf{v})=A\mathbf{v}$ on vector spaces
Shift operators on sequences: $T(f(n)))=f(n+1)$
…

An operator is a function that takes an input state and replaces it by an output state - one pattern replaced by another.

Some operators have the property that they reproduce themself / the pattern that gave rise to them. E.g. particles: A pattern that recreates itself a bit further away.