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Wronskian vs. Determinant in Determining Linear Independence?

  1. Jun 1, 2014 #1
    It seems to me that if a row is able to be zeroed out through Gaussian reduction that the determinate of that matrix would equal zero. Therefore, we know that at least one of equations/vectors that constructed the matrix was formed from the other two rows. That is -- that equation is dependent on the other two basis vectors.

    Why do we need the Wronskian to determine this?

    Thanks,
    Chris Maness
     
  2. jcsd
  3. Jun 1, 2014 #2

    SteamKing

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    The Wronskian is a special type of determinant used to determine if a set of solutions to a differential equation is linearly independent:

    http://en.wikipedia.org/wiki/Wronskian

    See the section on "The Wronskian and linear independence".
     
  4. Jun 1, 2014 #3
    Ok, is it that Wronskians are for function space where all the basis are formed by functions of x, where the determinants are for -- say -- {x,y,z} vectors in cartesian space?

    Chris
     
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