Prof. Max Tegmark first introduced the Fisher information matrix into cosmology in his paper titled Karhunen-Loeve eigenvalue problems in cosmology: How should we tackle large data sets?
As I read the paper, I noticed that Max utilized the following formula in deriving the Fisher matrix for the Gaussian case:
$$ \ln \text{det} \mathbf{C}=\text{Tr}\ln \mathbf{C}, $$
in which $\mathbf{C}$ is the covariance matrix, defined as $$ \mathbf{C} = \langle(\mathbf{x}-\mathbf{\mu})(\mathbf{x}-\mathbf{\mu})^t\rangle, $$ where $\mathbf{x}=\{x_0, x_1, x_2,\ldots\}$ is data, and $\mathbf{\mu}$ is the mean of data.
I don't understand at all why $\ln \text{det} \mathbf{C}=\text{Tr}\ln \mathbf{C}$ holds, and I haven't found any sources related to it. So how to derive this formula?
