Distortion of the spherical gaussian error through the canonical embedding in Ring - LWE
The section you quote is from the introduction. The paper goes into more technical detail later. For example, equation 3.1 states (roughly) the same equation, and then states that:
$$B = U\Sigma$$
Where $\Sigma$ is the matrix of the canonical embedding, expressed relative to the basis $\{\alpha_1,\dots, \alpha_n\}$, and $U$ is the matrix (defined on page 5):
$$
U = \begin{pmatrix}
I_{s\times s} &amp; 0 &amp; 0 \\
0 &amp; \frac{1}{\sqrt 2}I_{t\times t} &amp; \frac{i}{\sqrt 2}I_{t\times t}\\
0 &amp; \frac{1}{\sqrt 2}I_{t\times t} &amp; \frac{-i}{\sqrt 2}I_{t\times t}
\end{pmatrix}
$$
$U$ is unitary, and known to be an isomorphism $(H, \langle\cdot, \cdot\rangle_H)\cong (\mathbb{R}^n, \langle\cdot, \cdot\rangle)$, where $\langle x,y\cdot\rangle_H = \sum_i x_i\overline{y_i}$ is the Hermitian inner product, and $H$ is a certain conjugation-invariant subspace of $\mathbb{C}^n$ that contains the image of the canonical embedding.
This is all discussed on page 5.