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Getting a matrix

  1. Jan 16, 2014 #1
    Given a vector r = (x, y, z) is possible to make some manipulation for get the matrix:
    [tex]\begin{bmatrix} 0 & z & -y\\ -z & 0 & x\\ y & -x & 0\\ \end{bmatrix}[/tex]
    and this matrix too:
    [tex]\begin{bmatrix} x & 0 & 0\\ 0 & y & 0\\ 0 & 0 & z\\ \end{bmatrix}[/tex]
    ?
     
  2. jcsd
  3. Jan 16, 2014 #2

    Office_Shredder

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    What do you mean by "manipulation"? You just wrote those matrices down, you now have them to do whatever you want with them. Are you asking whether the map
    [tex] (x,y,z) \mapsto \left( \begin{array}{ccc} 0 & z & -y\\ -z & 0 & x\\ y & -x & 0 \end{array} \right) [/tex]
    is linear or something to that effect?
     
  4. Jan 16, 2014 #3
    manipulation in the sense of add, subtract, multiply, divide... algebraic/matrix manipulation
     
  5. Jan 25, 2014 #4
    I discovered how make the 1nd transformation!

    Let [r] the notation for the first matrix of my post #1, it's is given by: ##[\vec{r}] = \sqrt{\vec{r}\otimes \vec{r}-r^2 I}##

    However, I still dont know how get the second matrix...
     
  6. Jan 25, 2014 #5

    AlephZero

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    A hint:

    ##\begin{pmatrix} 1 & 0 & 0 \end{pmatrix} \begin{pmatrix} x \\ y \\ z \end{pmatrix} =
    \begin{pmatrix} x \end{pmatrix}##

    Then, use Kronecker products....
     
  7. Jan 27, 2014 #6
    Give me an example
     
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