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Hello everybody, Is there any explicit relation between the singular values $\lambda_X$ and $\lambda_Y$ of two same size matrices $X$ and $Y$, respectively, and the singular values $\lambda_{XY^t}$ of the matrix $XY^t$? Otherwise said, is there a function $f$ such that $\lambda_{XY^t}=f(\lambda_X , \lambda_Y)$? Thank you Riadh |
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No. It matters how the singular vectors interact. For example, let $X$ be the diagonal matrix with diagonal entries 1 and 2. Let $Y_1=X$, and let $Y_2$ be the diagonal matrix with diagonal entries 2 and 1. Then $XY_1$ and $XY_2$ have different singular values. However, if you have estimates on the singular vectors, you may get estimates on the singular values of the product. |
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