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Isomorphism definition

  1. Feb 1, 2016 #1
    1. The problem statement, all variables and given/known data
    I have a question about isomorphisms -- I'm not sure if this is the right forum to post this in though.

    A linear transformation is an isomorphism if the matrix associated to the transformation is invertable. This means that if the determinant of a transformation matrix = 0, then the transformation is not invertable and thus not an isomorph.

    Just wondering if this statement / conclusion is correct? Thanks :)

    2. Relevant equations


    3. The attempt at a solution
     
  2. jcsd
  3. Feb 1, 2016 #2

    Samy_A

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    Looks correct (as you talk about matrices, the implicit assumption is that we are talking about a finite dimensional vector space).

    EDIT: there is a typo: it must be invertible.
     
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