Having a bit of trouble with the simplification in one of problems in the chapter 2.5 exercise #42, specifically how do you get from I - UV +U(I - VU)^(inverse)V-UVU(I - VU)^(inverse)V to I -UV + U(I-VU)(I-VU)^(inverse)V ? It's clear this simplifies to I but I'm not seeing from step 2 to 3. This is solution #42 at the top of page 523 in the text. Thanks!

Question

Having a bit of trouble with the simplification in one of problems in the chapter 2.5 exercise #42, specifically how do you get from I - UV +U(I - VU)^(inverse)V-UVU(I - VU)^(inverse)V to I -UV + U(I-VU)(I-VU)^(inverse)V ?  It's clear this simplifies to I but I'm not seeing from step 2 to 3.  This is solution #42 at the top of page 523 in the text.  Thanks!

datanewb · Answer

I've broken down the process between steps 2 and 3.  Let me know if you need more clarification.

anonymous · Answer

Excellent. Step 2a was exactly what I was missing/didnt see myself. Thank you very much.