Singular Value Decomposition Question - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-25T19:37:01Z http://mathoverflow.net/feeds/question/112613 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/112613/singular-value-decomposition-question Singular Value Decomposition Question mark leeds 2012-11-16T21:04:37Z 2012-11-16T21:24:48Z <p>Hi: I'm new to this list so apologies if I do anything wrong with my question.</p> <p>Suppose I have a matrix $Y$ whose SVD can be decomposed as $Y = U_{0}\Sigma_{0}V_{0}^{*} + U_{1}\Sigma_{1} V_{1}^{*}$ where $U_{0}$ and $V_{0}$ are the singular vectors associated with the singular values greater than $\tau$ and<br> $U_{1}$ and $V_{1}$ are the singular vectors associated with singular values greater than $\tau$.</p> <p>The paper then goes on to say that $U_{0}^{*} U_{1}\Sigma_{1} V_{1}^{*} = 0$ and $U_{1}\Sigma_{1} V_{1}^{*}V_{0} = 0$. </p> <p>Could someone explain why the last two claims are true ? </p>