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Solving a non linear system

  1. Jun 5, 2010 #1
    Hello all,
    i would like to ask you how can be solved this system: X'*X=A, where A (pxp) known Matrix and X(nxp) the matrix i want to compute.

    Thanks in advance
     
  2. jcsd
  3. Jun 5, 2010 #2
    I'm not sure of the best way to solve this but, if I'm interpreting what you wrote correctly, you can get an implicit solution like

    [tex]
    \dot{X}^{\dagger }X=A
    \Longrightarrow \dot{X}^{\dagger }X+X^{\dagger }\dot{X}=A+A^{\dagger }
    [/tex]
    [tex]
    \Longrightarrow \partial _t\left(X^{\dagger }X\right)=A+A^{\dagger }
    [/tex]
    [tex]
    \Longrightarrow X^{\dagger }X=\int _0\left(A+A^{\dagger }\right)dt+X_0^{\dagger }X_0
    [/tex]
     
  4. Jun 11, 2010 #3
    [tex]X=U\Sigma V^T,X^T X=V\Sigma^T U^TU\Sigma V^T=V\Sigma^2 V^T=A[/tex]

    [tex]V\Sigma V^T\in X[/tex]
     
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