Having difficulty understanding what the Range of a linear transformation is.

[phantomcow2]

One of the topics in my linear algebra course is kernel and range of a linear transformation. I have a firm understanding of what the kernel is: the set of vectors such that it maps all inputs to the zero vector. Range, however, remains nebulous to me. My textbook says that the range is "THe set of all vectors in W that are images under T of at least one vector in V."

I'm not sure what it means to be "an image under T." Could somebody explain this to me? I'd just like to have this concept clarified. Thanks.

 

[Newtime]

One of the topics in my linear algebra course is kernel and range of a linear transformation. I have a firm understanding of what the kernel is: the set of vectors such that it maps all inputs to the zero vector. Range, however, remains nebulous to me. My textbook says that the range is "THe set of all vectors in W that are images under T of at least one vector in V."

I'm not sure what it means to be "an image under T." Could somebody explain this to me? I'd just like to have this concept clarified. Thanks.

See the attachment.

 

[phantomcow2]

Wow, that is a wordy explanation and exactly what I needed. Thanks :).

 

[radou]

The range and image are the same thing. But the codomain isn't. If a mapping is surjective, then they're all the same set, but in general, not.