Hi: I'm new to this list so apologies if I do anything wrong with my question.

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

$U_{1}$ and $V_{1}$ are the singular vectors associated with singular values
greater than $\tau$.

The paper then goes on to say that $U_{0}^{*} U_{1}\Sigma_{1} V_{1}^{*} = 0$ and $U_{1}\Sigma_{1} V_{1}^{*}V_{0} = 0$.

Could someone explain why the last two claims are true ?