because \(U_K\) only has \(K\) columns , and \(S^{(K)}V^\top\) only has \(K\) rows, so their product is an outer product of two narrow matrices, so the rank is at most \(K\). rank can be less than \(K\), but surely not more.
Hey, in the same topic, \(S^K\) is a DxN Matrix, and Uk is a DxK matrix, so how can we multiply Uk and S^K? is it well defined? because it is DxK * DxN which is not defined.
Thanks in advance,
SVD
Hey, why the rank of this matrix is K? I don't know how to prove it:(
Thanks,
because \(U_K\) only has \(K\) columns , and \(S^{(K)}V^\top\) only has \(K\) rows, so their product is an outer product of two narrow matrices, so the rank is at most \(K\). rank can be less than \(K\), but surely not more.
1
Hey, in the same topic, \(S^K\) is a DxN Matrix, and Uk is a DxK matrix, so how can we multiply Uk and S^K? is it well defined? because it is DxK * DxN which is not defined.
Thanks in advance,
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