With reference to the following definition of GMM (see snapshot from Reynolds (1)),
I have two doubts:
In the definition of probability density, the covariance matrix (denoted by sigma) is represented as a vector (since it is represented in bold letters) for each component density. How is it possible? In my opinion, there must be a single covariance matrix (as a scalar and not as a vector) for each component densities.
Secondly, is my interpretation correct when I say that the mean vector (denoted by $mu$) will also be $D$ dimensional if the the data vector $x$ is $D$ dimensional for each component density?
I also think that the order of covariance matrix must be $D\times D$. Correct me if I am wrong.
(1): Douglas Reynolds,
"Gaussian Mixture Models"
MIT Lincoln Laboratory