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Questions about the properties of vector spaces and linear transformations, including linear systems in general.

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does the basis in the singular value decomposition of a sum depend on the singular values of...

Suppose you have 4 matrices with singular value decompositions $A = U_1 \Sigma_A V_1^{\dagger}$, $B = U_2 \Sigma_B V_2^{\dagger}$, $C = U_1 \Sigma_C V_1^{\dagger}$ and $D = U_2 \Sigma_D V_2^{\dagger}$ …