I was wondering if anyone could shed some light on interpreting multivariate Gaussian notation with more than 2 parameters as arguments. For instance in some papers I see the following notation $\mathcal{N}(\mathbf{y}; \hat{\mathbf{y}}(\mathbf{x}, \mathbf{\omega}), \tau^{-1}\mathbf{I}_{D})$ which I interpret as the Gaussian of variable $\mathbf{y}$ parameterised with mean = $\hat{\mathbf{y}}(\mathbf{x}, \mathbf{\omega})$ and variance = $\tau^{-1}\mathbf{I}_{D}$.

Am I reading/interpreting this correctly?

But I've also seen the following notation as well $\mathcal{N}(\mathbf{A}, \mathbf{\Lambda}, \mathbf{U})$ in some other papers which I don't know how to read or interpret it.

Is this a valid notation of having a multivariate Gaussian with more than 2 parameteres (mean, variance) and how to go about interpreting or reading that notation.

If you could point me to some other resources explaining these notations I would be grateful?