You may use the division symbol. If $\alpha = (\alpha_1 ,\ \alpha_2 ,\ \cdots ,\ \alpha_n)$ and $\beta = ( \beta_1 ,\ \beta_2,\ \cdots ,\ \beta_n)$ are bases, then the matrix representing the change-of-base from $\alpha$ to $\beta$ is denoted by $$\frac \alpha \beta \ \ \ \ \text{or}\ \ \ \ \beta \backslash \alpha,$$
but **not** $\alpha / \beta$.

This notation has some benefits: for example we may write $v = \alpha x$ to say that $v$ is the linear combination $x_1 \alpha_1 + x_2 \alpha_2 + \cdots + x_n \alpha_n$ of the base $\alpha$ by the coefficient (column) vector $x = [x_1 \ x_2 \ \cdots \ x_n]^T$. Then it is natural to use symbols like
$$ x = \frac v \alpha \ \ \ \ \text{or} \ \ \ \ \alpha \backslash v. $$
Now suppose $y = [y_1 \ \cdots \ y_n]^T$ is the coordinate column vector of $v$ w.r.t. the base $\beta$. Then now we can write
$$ y = \frac \alpha \beta x, \ \ \ \ \text{that is,} \ \ \ \ \frac v \beta = \frac \alpha \beta \frac v \alpha \ \ \ \ \text{or} \ \ \ \ \beta \backslash v = (\beta \backslash \alpha)(\alpha \backslash v). $$
Be careful to perform cancellation along the line $\backslash$, not $/$.

We may define several similar symbols to make things involving change-of-base easy.