- #1

- 1

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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

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- Thread starter sa_christina
- Start date

- #1

- 1

- 0

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

- 313

- 1

[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

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[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]

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

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