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Jiawei Liu
Jiawei Liu
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Jiawei Liu
Jiawei Liu
  • 33
  • 4

Suppose we have an M$\times$N complex matrix $H$ and its singular value decomposition $H=U\Lambda V^*$ and an N$\times$N covariance matrix $R_s$ with its eigendecomposition $R_s = U_s\Lambda_sU_s^*$. We also have the eigendecomposition of $HR_sH^*$ as $U_A\Lambda_AU_A^*$. In my research problem setting, I know $U_A$, $H$ but not $R_d$$R_s$ and $\Lambda_A$. I want to solvefind $U_s$ using $H$ and $U_A$. I was wondering if there exists any connection between them.

Suppose we have an M$\times$N complex matrix $H$ and its singular value decomposition $H=U\Lambda V^*$ and an N$\times$N covariance matrix $R_s$ with its eigendecomposition $R_s = U_s\Lambda_sU_s^*$. We also have the eigendecomposition of $HR_sH^*$ as $U_A\Lambda_AU_A^*$. In my research problem setting, I know $U_A$, $H$ but not $R_d$ and $\Lambda_A$. I want to solve $U_s$ using $H$ and $U_A$. I was wondering if there exists any connection between them.

Suppose we have an M$\times$N complex matrix $H$ and its singular value decomposition $H=U\Lambda V^*$ and an N$\times$N covariance matrix $R_s$ with its eigendecomposition $R_s = U_s\Lambda_sU_s^*$. We also have the eigendecomposition of $HR_sH^*$ as $U_A\Lambda_AU_A^*$. In my research problem setting, I know $U_A$, $H$ but not $R_s$ and $\Lambda_A$. I want to find $U_s$ using $H$ and $U_A$. I was wondering if there exists any connection between them.

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Jiawei Liu
Jiawei Liu
  • 33
  • 4

Connections between eigenvectors after matrix multiplication

Suppose we have an M$\times$N complex matrix $H$ and its singular value decomposition $H=U\Lambda V^*$ and an N$\times$N covariance matrix $R_s$ with its eigendecomposition $R_s = U_s\Lambda_sU_s^*$. We also have the eigendecomposition of $HR_sH^*$ as $U_A\Lambda_AU_A^*$. In my research problem setting, I know $U_A$, $H$ but not $R_d$ and $\Lambda_A$. I want to solve $U_s$ using $H$ and $U_A$. I was wondering if there exists any connection between them.