Given $Q(\mathbf{B}) = \mathcal{N}(\mathbf{M},\mathbf{C}_1 \otimes \mathbf{C}_2)$ where $\mathbf{M} = \mathbf{m}_1 \otimes \mathbf{m}_2$, $\mathbf{B} \in \mathbb{R}^{n \times k}$, $\mathbf{m}_1 \in \mathbb{R}^n$, $\mathbf{m}_2 \in \mathbb{R}^k$, $\mathbf{C}_1 \in \mathbb{R}^{n \times n}$, $\mathbf{C}_2 \in \mathbb{R}^{k \times k}$ and $\otimes$ denotes outer product. How can I find $E_Q[\ln \mathcal{N}(\mathbf{B} \mid \mathbf{o}_1 \otimes \mathbf{o}_2,\mathbf{D}_1 \otimes \mathbf{D}_2)]$ where $E$ is the expectation and $\mathcal{N}$ denotes normal distribution?
Edit 1: In $E_Q[\ln \mathcal{N}(\mathbf{B} \mid \mathbf{o}_1 \otimes \mathbf{o}_2,\mathbf{D}_1 \otimes \mathbf{D}_2)]$, '$\mid$' denotes conditioned