What's the difference between a function and an operator?

>>7974898
I'm also interested in this as someone who doesn't have a math background

>>7974898
Operators are specifically between vector spaces

functions can map between any two sets

All operators are functions but not all functions are operators. A function which maps a piece of fruit to its colour is not an operator.

>>7974898

Function:
> x + y = z

Operator:
> +

>>7975036
this is just a simple case of
>>7975013

It's not like plain operator has a super strictly defined meaning, but usually you reserve operator for functions that map between somewhat similar structures.

(Of course, we speak of functions in full generality now - some sort of map between sets - but then we'd have to fight with these spergs who'd insist the Dirac delta "isn't really a function", those for whom function is just maps from C to C and restrictions of that.)

>>7975013
Is it possible to have non-linear operators operating on vector spaces? I've only ever seen linear operators used so I wondering how non-linear ones would even look like.

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155KB, 459x306px

>>7975028

>>7975343
Once you know what linear transformations are, rotations, stretching, shearing, (translation in homogeneous coordinates only), then you will understand what isn't a linear transformation.

y=x^2 is not a linear transformation.

There are tons of conformal maps that are nonlinear and of use from complex analysis, check those out.