Proving the Properties of Pseudo Inverse and Transpose

[ahamdiheme]

I have been battling with this for hours now, i just keep getting stuck.
It is to show that:
(xy^T)⁺=(x^Tx)⁺(y^Ty)⁺yx^T

After expanding the left side, leting xy^T=A. I get stuck at (yx^Txy^T)⁺yx^T

I have tried from both sides of the equation, but can't arrive at the expected result. Any clues?

 

[zyh]

I tried for 20 minutes, and can't figure it out. But I think you can refer to: http://en.wikipedia.org/wiki/Moore-Penrose_pseudoinverse.
By the way, does the x and y are arbitrary matrix?

 

[ahamdiheme]

I got it. All that needs to be done is to show that it satisfies the four penrose properties which state that (1) AGA=A
(2) GAG=G
(3) (AG)^T=AG
(4) (GA)^T=GA
By letting A=xy^T and G=the right hand side, this can easily be proved.
Thanks for the effort anyway.