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Block Diagonalization. SVD of matrix

Agness
in Linear Algebra and Group Theory

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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:

1.PNG.8e3b891af40e844f5c5b0e65251c99a4.PNG
Now I would like to calculate HP, where P is a projection matrix into the null space of H.

2.PNG.d64128494945dd6cc8c400219f3ffc6f.PNG

Question 1: What means4.PNG.ad8eec2a3fc40d64f61f54c4598c1f76.PNG?

**My suggestion:**
4.PNG.ad8eec2a3fc40d64f61f54c4598c1f76.PNG = 1/2 (1 1 1 1), it is the first row V^H

Question 2: Can someone explain me this

3.PNG.938be985b440ee615c21c73ea7e33da9.PNG

 

PS please provide me the exaples

 

 

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