I am going through this talk [Fully Homomorphic Encryption from LWE] (pg 96, 102). And I am a bit confused by how the resulting ciphertext for the multiplicative homomorphism example is derived. I think it's mostly notation throwing me off.
It seems $\mathbf{A}$ is a random matrix $\in \mathbb{Z}_{q}^n$, and the resulting ciphertext $\mathbf{a}$, is a vector of size $n$.
Where $\mathrm{a} = \sum h_i \cdot \mathbf{A}_i + \sum h_{i,j} \cdot \mathbf{A}_{i,j}$
Are the dimensions of $(\sum h_i \cdot \mathbf{A}_i)$ a vector of size $n$ and $(\sum h_{i,j} \cdot \mathbf{A}_{i,j} )$ a scalar?