Function vs mapping vs transformation

[uiulic]

During learning linear algebra, I have met at least three items (kind of action in my own word): function, mapping and transformation. What are the relation and difference among them?

e.g. Given y=f(x), we can say f map x to y, f transform x to y and the function of x is y.

In saying the function of x is y, we sometimes also say y is a function of x. And in this case, we can also write y=y(x). In y=y(x), the second y is actually the action of the function. I get a little confused by the expression y=y(x). But there seems no confusion when using "mapping" instead of function. Is this why you choose " mapping" etc in learning further mathematics...?


Thanks

 

[matt grime]

There is no difference - some just tend to be used in different situations. One would never say a 'linear function' but would use linear map and linear transformation interchangably.

As for y=y(x), you should not think of that as an equation, but as an assignment (we are saying y is y(x)).

 

[uiulic]

There is no difference - some just tend to be used in different situations. One would never say a 'linear function' but would use linear map and linear transformation interchangably.

As for y=y(x), you should not think of that as an equation, but as an assignment (we are saying y is y(x)).

Thanks for the clarification. But "linear function" is the word I often meet, even in Shilov's book (Linear algebra,Dover 1977).