I am trying to normalize 4x4 matrix (g and f are functions):(adsbygoogle = window.adsbygoogle || []).push({});

\begin{equation}

G=\begin{matrix}

(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)

\end{matrix}

\end{equation}

It's a matrix that's in a research paper (which I dont have) which gives the normalization constant as: N=4-2g^2+2f^2.

I've been looking up online and found that N can be found with:

method 1: N=\sqrt{\sum{X^2}} where X represents the elements of the matrix.

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

method 3: The ratio between the integral of excited state matrix and the integral of normal state of the matrix.

I'm not sure who's right, but I'm not getting what was on paper.

For method [1] I'm getting as far as: N^2 = 4(1+f^4+f^2g^2+f^2) . 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.

Note that the normalization must satisfy the following condition G^2=1

Any comments about all methods mentioned and how to implement it?

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# A Normalization of 4x4 matrix

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