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Operator equation

  1. Apr 4, 2010 #1
    A mathematical operator (Aop) operates on a function (f) to generate a new function (f '):
    Aop (f) = f ' (1)

    Consider that I subtract a from b to get c:
    b-a = c (2)

    Can I write this subtraction operation as an operator equation of the form (1) as shown below?

    (-a) (b) = c (3)

    where (-a) represents the operator "subtract a".

    Similarly for +, x and /.
     
  2. jcsd
  3. Apr 4, 2010 #2

    MathematicalPhysicist

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    Gold Member

    Yes, you can be it won't be a linear operator like taking a derivative (if that's what ' represents), at the most it's an affine function.
     
  4. Apr 4, 2010 #3
    You can write either as:

    1) A bilinear operator, that is, one that takes as inputs pairs of arguments: A(a,b)=a-b. In this case, your -a is A(a,...).

    2) Directly, like you propose, but then you have a family of operators, one for each a, or an affine operator, for a fixed a.
     
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