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Math Help - [SOLVED] matrix manipulation

  1. #1
    jcrennes2
    Guest

    [SOLVED] matrix manipulation

    hi everyone,

    I have a vector u=(x y z) and I would like to transform it (by some linear manipulations) into the following matrix:
    (x 0 0)
    (0 y 0)
    (0 0 z)

    in matlab notation: [x 0 0; 0 y 0; 0 0 z]

    Concretely I would like to find some matrices A and B, for example, such that:
    [x 0 0; 0 y 0; 0 z 0]=A*[x y z]*B

    I know that there exists the function diag() in matlab but I would like to use some linear relations to build such a matrix.

    Is there somebody that could help me?


    Thank you very much

    JC
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  2. #2
    Senior Member
    Joined
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    Quote Originally Posted by jcrennes2 View Post
    hi everyone,

    I have a vector u=(x y z) and I would like to transform it (by some linear manipulations) into the following matrix:
    (x 0 0)
    (0 y 0)
    (0 0 z)

    in matlab notation: [x 0 0; 0 y 0; 0 0 z]

    Concretely I would like to find some matrices A and B, for example, such that:
    [x 0 0; 0 y 0; 0 z 0]=A*[x y z]*B

    I know that there exists the function diag() in matlab but I would like to use some linear relations to build such a matrix.

    Is there somebody that could help me?


    Thank you very much

    JC
    It cannot be done. The reason is this

    Theorem: The rank of matrix AB is less than or equal to the rank of either A or B.

    U = [x,y,z] is a 1x3 matrix of rank 1.

    M = \begin{bmatrix} x & 0 & 0 \\ 0 & y & 0 \\ 0 & 0 & z \end{bmatrix} is a matrix of rank 3 (assuming the diagonal entries are non-zero).

    Because of the theorem, there is no series of matrices you can multiply U by to increase the rank from 1 to 3. After every multiplication, the rank will be less than or equal to 1.
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