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Tagged with matrix-congruences svd
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Show the relation between singular values of $A$ and $B^*AB$
Proposition: For any nonsingular $A\in\mathbb{C^{n\times n}}$ and nonsingular $B\in\mathbb{C^{n\times n}}$, the following holds
$$\frac{\Re(x_i^*Ax_i)}{\sigma_i(A)}=\frac{\Re(y_j^*B^*ABy_j)}{\sigma_j(...
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