Understanding Linear Mapping: A Non-Technical Explanation

[Cardebaun]

Hello,

so i was looking up the definition of linear mapping and mapping in general and i have seen the technical definition a few times but i was wondering if someone would mind explaining it to me in more general english. How would you explain it instead of just pointing out the definition?

What i have gotten so far is that it is an operation performed to transfer(not sure if I'm using this word in the correct mathematical sense) an equation to another vector space.

please correct me if I'm wrong thanks.

 

[HallsofIvy]

A "mapping" from one set to another is any function or relation that associates every member of the "domain" set to a member of the "range" set.

To have a linear mapping, you need vector spaces rather than general sets so that you can define "ax+ by" for numbers a and b and vectors x and y. Then a mapping is "linear" if and only if f(ax+ by)= af(x)+ bf(y).