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  1. M

    Linear operator

    Sorry but I think that you didn't read my post. I defined multiplication operator which goes from ##f## to ##5f##.
  2. M

    Linear operator

    I define A as multiplicative operator clearly.
  3. M

    Linear operator

    Linear operator A is defined as A(C_1f(x)+C_2g(x))=C_1Af(x)+C_2Ag(x) Question. Is A=5 a linear operator? I know that this is just number but it satisfy relation 5(C_1f(x)+C_2g(x))=C_15f(x)+C_25g(x) but it is also scalar. Is function ##A=x## linear operator? It also satisfy...
  4. M

    Can you explain me why this is also isomorphism?

    I know that. But I asked only for logarithm because \log (ab)=\log (a)+\log (b) \log ((-a)(-b))=\log (a)+\log (b) Why function ##f(x)=e^x## isn't surjective?
  5. M

    Can you explain me why this is also isomorphism?

    Homomorphism is defined by ##f(x*y)=f(x)\cdot f(y)##. One interesting example of this is logarithm function ##log(xy)=\log x+\log y##. Can you explain me why this is also isomorphism?
  6. M

    Eigenvalue question

    Is there some easy way to see that?
  7. M

    Eigenvalue question

    If ##\hat{A}\vec{X}=\lambda\vec{X}## then ##\hat{A}^{-1}\vec{X}=\frac{1}{\lambda}\vec{X}## And what if ##\lambda=0##?
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