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Thread: Matrix transformation

  1. #1
    Member
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    Matrix transformation

    If we want:


    \[
    \frac{1}{3}
    \begin{bmatrix}
    1 & 1 & 1 \\
    1 & a & a^2 \\
    1 & a^2 & a
    \end{bmatrix}
    =
    \frac{1}{3}
    \begin{bmatrix}
    1 & 1 & 1 \\
    1 & b^2 & b \\
    1 & b & b^2
    \end{bmatrix}
    \]

    And $\displaystyle a = e^{\frac{2\pi i}{3}}$, how much is $\displaystyle b$ to fulfill the condition?

    So if I cancel $\displaystyle \frac{1}{3} $on both sides and try to get the inverse of one matrix I don't get $\displaystyle b = e^{\frac{-2\pi i}{3}}$ which is correct.

    Thanks for the help.
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  2. #2
    Super Member
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    Re: Matrix transformation

    Two matrices are equal only if they have the same dimensions and then all corresponding elements are equal.

    So here, you need
    a = b^{2}
    and
    b = a^{2}
    .
    Thanks from topsquark, Nforce and HallsofIvy
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  3. #3
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    Re: Matrix transformation

    Ok, maybe I don't understand, can you extrapolate thinking because the answer is $\displaystyle b = e^{\frac{-2\pi i}{3}}$. I don't know how do we get to there, do you see the problem?
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  4. #4
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    Re: Matrix transformation

    $\displaystyle a^{2} = e^{\frac{4\pi\imath}{3}}=e^{\frac{-2\pi\imath}{3}}$
    Last edited by BobP; Oct 19th 2018 at 08:54 AM.
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