Clarification to the text page 387

[Samuele7F]

Dear Professor, there is a part of the following text that I don't understand.

We said that Xtilde=GH' and that Xtilde=GV', but then H=V*gamma.
Shouldn't H be equal to V ?
I kindly ask you to explain this mathematical step to me.

If this new H is the name of a parallel example unrelated to the previous H, as I think it is, I suggest finding another name because it can cause misunderstandings.
Thank you.

[MarcoRianiUNIPR]

In (11.13) we say that $\tilde X$ (which is the product of 3 matrices $U$ $\Gamma$ and $V'$) can be expresses as the product of two matrix $G$ and $H'$.
In the prose below we discuss the implications if the second matrix is $\Gamma$ is part of $G$ or is part of $H$.

If $H'= V'$ then $G= U \Gamma$

If $H' = (\Gamma V)'$ then $G= U$

Please let me know

[Samuele7F]

Ok thank you very much, now I get it