# Pseudo Inverse and Transpose

1. Nov 8, 2008

### ahamdiheme

I have been battling with this for hours now, i just keep getting stuck.
It is to show that:
(xyT)+=(xTx)+(yTy)+yxT

After expanding the left side, leting xyT=A. I get stuck at (yxTxyT)+yxT

I have tried from both sides of the equation, but cant arrive at the expected result. Any clues?

Last edited: Nov 8, 2008
2. Nov 20, 2008

### zyh

3. Nov 21, 2008

### 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=xyT and G=the right hand side, this can easily be proved.
Thanks for the effort anyway.