how to solve this problem？

For this question, I have proved that it is decreasing, but how to prove its limit?

how to solve this problem?

relation and function: for this question, how to solve it?

In this question, how can I find out the eigenvalues?

How to prove in this question?

How to prove part b and c?

To prove or disprove this question: for part b), can I prove as : because X^(T)X=0, so X^(T)=0 or X=0, it implies that X=0. And if my proof is true , does it can apply to the part c)?

Wanna ask how to solve this question?

how can i get the formula