Talk:Linear map

Major fixing needed

1. This page is lifted from Wikipedia, but for some reason, parts of the Wikipedia page were deleted.
2. The definition is terrible. First, every linear algebra book I have seen defines the term as "linear transformation", using map as an informal substitute afterward. But googling "linear map" and "linear transformation" shows "linear map" is much more prevalent. Perhaps because I am wrong, but more likely because people are too lazy to type "transformation"? In any case, I think the page name and main term should be "transformation", not "map", just based on my experience. Does anyone have a much different experience?
3. Transformation does not usually refer to a map from a space to itself. Transformation is the most general term, and "operator" has a tendency to refer to a map from a set to itself. This is based on my own experience, but to back me up, here is the American Heritage Dictionary[1]

I thought I was going crazy when I looked up the definition of "operator" given on Wikipedia, saying inputs and outputs must be functions, but even there, the inputs and outputs are drawn from the same set. Can anyone back me up? Or is my experience rather unusual, and other places/cultures/books use transformation as written here and operator for more general maps?