What Happens to Av^j When j Exceeds Rank r in SVD?

[stuck_on_math]

Let A be an m × n matrix of rank r and let A = U$$\Sigma$$V be an SVD of A. Prove that

Av$$^{j}$$= sigma^j* u$$^{j}$$ for 1<=j<=r

What is Av^j for r + 1<=j<=n?

 

[CompuChip]

Well, what do you think?

 

[stuck_on_math]

I don't know, that's why I am asking

 

[FunkyDwarf]

You must have some idea.

 

[stuck_on_math]

I really don't