Hubbard's & Hubbards Concrete To Abstract Function

  1. Hubbard's & Hubbards "Concrete To Abstract" Function

    On page 215 of H&H Vector Calculus, Linear algebra and Differential Forms text the authors define something they call the "concrete to abstract function". It is defined as follows:

    Let (x_1, ..., x_m) be a point in R^m and let {v_1, ..., v_m} be a set of vectors in V. The, the abstract to concrete function F is given by

    F(x_1, ..., x_m) = x_1*v_1 + ... + x_m*v_m.

    Is there another name/ standardized name for this function?

    Thanks
     
  2. jcsd
  3. Re: Hubbard's & Hubbards "Concrete To Abstract" Function

    The dot product?
     
  4. Re: Hubbard's & Hubbards "Concrete To Abstract" Function

    No...It's not a scalar product because the result is a vector, not a number; it's a mapping from R^m to V.
     
  5. Re: Hubbard's & Hubbards "Concrete To Abstract" Function

    Ah good point
     
  6. Re: Hubbard's & Hubbards "Concrete To Abstract" Function

    I don't see anything special about it; it's just a linear map from Rm to V that takes ei (the ith standard basis vector in Rm) to vi.
     
Know someone interested in this topic? Share a link to this question via email, Google+, Twitter, or Facebook
Similar discussions for: Hubbard's & Hubbards Concrete To Abstract Function
Loading...