content_image/314139.jpg content_image/314140.jpg content_image/314141.jpg content_image/314145.jpg
it follows that G can be chosen to be symmetric without loss of generality. It can therefore be diagonalized by a unitary transformation. Define the diago- nalized metric as 

<img src='content_image/314139.jpg'>

where U is the unitary matrix whose rows are the (normalized) eigenvectors of G . Note that 

Consider 

<img src='content_image/314140.jpg'>

<img src='content_image/314141.jpg'>

Since det G = det G , from above, and, trivially from the definition, ln det G = Tr ln G , we have that (where G$_{i}$ is the i th eigenvalue) 

<img src='content_image/314145.jpg'>

