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Can a Transformation Matrix be one-to-one and not onto?

  1. Aug 12, 2010 #1
    Title says all..
    A transformation matrix is one to one if its columns are linearly independant, meaning it has a pivot in each column
    but what if it doesnt have a pivot in each row(i.e. not onto)? is it still one-to one?
  2. jcsd
  3. Aug 12, 2010 #2
    actually nvm,... I just realized it will map an Rn vector onto Rm where m < n, but its still one-to-one
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