# Notation for matrix filled with zeros except for one row and one column

Is there existing succinct notation for a matrix $$[A]_i$$ whose elements are all $$0$$, except that the $$i$$th row and $$i$$th column is given by a particular vector, for example the vector

$$\mathbf{z} = \frac{\mathbf{v} - 2\mathbf{v}_i}{a}$$

I'm trying to avoid having to put in something like

$$[A]_i = \begin{bmatrix} 0 & \ldots & \dfrac{\mathbf{v}_1 - 2\mathbf{v}_i}{a} & 0 & \ldots & 0 \\ \vdots & \ddots & \dfrac{\mathbf{v}_2 - 2\mathbf{v}_i}{a} & 0 & \ldots & 0 \\ \vdots & \vdots & \vdots & \vdots & \vdots & \vdots \\ \dfrac{\mathbf{v}_1 - 2\mathbf{v}_i}{a} & \dfrac{\mathbf{v}_2 - 2\mathbf{v}_i}{a} & \ldots & \ldots & \ldots & \dfrac{\mathbf{v}_n - 2\mathbf{v}_i}{a} \\ 0 & \ldots & \dfrac{\mathbf{v}_{i+1} - 2\mathbf{v}_i}{a} & 0 & \ldots & 0 \\ \vdots & \vdots & \vdots & \vdots & \vdots & \vdots \\ \end{bmatrix}$$

If $${\bf e_i}$$ is the column vector with $$1$$ in position $$i$$ and $$0$$ elsewhere, this is $${\bf z} {\bf e_i}^\top + {\bf e_i} {\bf z}^\top - z_i {\bf e_i} {\bf e_i}^\top$$.
$$M_{y, x}= \begin{cases} x = i & \dfrac{v_y - 2v_i}a \\ y = i & \dfrac{v_x - 2v_i}a \\ \text{else} & 0 \\ \end{cases}$$