Block Diagonalization. SVD of matrix

[Agness]

I need really your help. I am trying to understand block diagonalization algorithm for multi-user MIMO system. But I guess My main problem is I don't understand the mathematics apparat of calculation SVD and other stuff.
let's assume that the channel matrix looks like:

Now I would like to calculate HP, where P is a projection matrix into the null space of H.

Question 1: What means?

**My suggestion:**
= 1/2 (1 1 1 1), it is the first row V^H

Question 2: Can someone explain me this

 

PS please provide me the exaples