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Taylor Expansion on Determinant

  1. Nov 2, 2013 #1
    1. The problem statement, all variables and given/known data

    Show by direct expansion that:

    det (I + εA) = 1 + εTr(A) + O(ε2)

    2. Relevant equations

    f(x) = f(a) + (x-a)f'(a) + (1/2)(x-a)2f''(a) + ...

    3. The attempt at a solution

    Does the question mean Taylor expansion when they say 'direct expansion'?

    I'm kind of stuck on how to differentiate a determinant.

    Expanding det (I + εA) about det (I) :

    det (I + εA) = det(I) + [det (I + εA) - det(I)]f'(x) + ...

    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Nov 2, 2013 #2

    UltrafastPED

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