Definition · applies to functions

High school

A transform turns a function into another function, often to reveal hidden information or make a problem easier.

Undergraduate

A transform is an operator, usually an integral operator, that converts a function of one variable into a function of another variable.

Examples

Non-examples

Things that may be mistaken for examples.

  • $f(x) = x^2$ on $\reals$ High school
    $f(x) = x^2$ on $\reals$ is not a transform, because its inputs are numbers, not elements of a space of functions.

Notes

“Transformation” also means a map from a space to itself, such as a rotation or a linear transformation. That usage is broader.

All definitions · All distinctions · All examples