Hi All!

This is my first time putting up my own thread on MF. I can usually find what I'm looking for, but this time: no go.

As the title says, I'm trying to find the normalization constant of this 4x4 matrix (g and f are functions):

(1-g^2) 0 0 0

0 (1+f^2) (-g^2-f^2) 0

0 (-g^2-f^2) (1+f^2) 0

0 0 0 (1-g^2)

It's a matrix that's in a research paper which gives the normalization constant (they use the word 'factor'. I'm not sure if that means something diff.) as: N=4-2g^2+2f^2.

1]I've been looking up online and found that N can be found with: N=\sqrt{\sum{X^2}} where X represents the elements of the matrix.

2]I also found somewhere which said that I need to find the determinant.

I'm not sure who's right, but I'm not getting what's in the paper.

For method [1] I'm getting as far as: N^2 = 4(1+f^4+f^2g^2+f^2) and got stuck trying to find the square root (it's been a while since I've done multinomial theorem). So I backtracked to see if their N^2 matches my N^2. But their N^2=16+4g^4+4f^4+16g^2-8g^2f^2+16f^2.

and method [2] is giving me something so long, with so many variables of (g^2), (f^2), (g^4), (f^4),(g^2f^4) (and it keeps going for about 3tysomething variables) that I've given up.

So I'm wrong all over the place.

Can someone help me out?

booklist05 confused