Solving a non linear system

  • #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
 

Answers and Replies

  • #2
313
1
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]
 
  • #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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