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I have been struggling with this problem for a while, and I have not found the answer in textbooks or google. Any help would be very much appreciated.

Suppose I know the singular value decomposition of matrix B, which is a singular, circulant matrix. That is, I know [tex]u_i[/tex], [tex]v_i[/tex], and [tex]\sigma_i[/tex], such that [tex]BB^*v_i = \sigma_i^2v_i[/tex] and [tex]B^*Bu_i = \sigma_i^2u_i[/tex]. Where [tex]B^*[/tex] is the conjugate transpose.

Now let A = DB, where D is a diagonal matrix. Is there any way to determine the singular values and vectors of A from the singular values and vectors of B?

Thank you,

Jason

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# Singular values of a matrix times a diagonal matrix

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