Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

  1. Apr 20, 2010 #1
    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.
     
  2. jcsd
  3. Apr 20, 2010 #2
    See the attachment.
     

    Attached Files:

  4. Apr 21, 2010 #3
    Wow, that is a wordy explanation and exactly what I needed. Thanks :).
     
  5. Apr 21, 2010 #4

    radou

    User Avatar
    Homework Helper

    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.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook