Singular Value Decomposition Question - MathOverflow most recent 30 from http://mathoverflow.net2013-05-25T19:37:01Zhttp://mathoverflow.net/feeds/question/112613http://www.creativecommons.org/licenses/by-nc/2.5/rdfhttp://mathoverflow.net/questions/112613/singular-value-decomposition-questionSingular Value Decomposition Questionmark leeds2012-11-16T21:04:37Z2012-11-16T21:24:48Z
<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>