Name for "interleaving" or "all-combinations" of two vectors

Question

Is there a name for combining two vectors $\vec{x} = \begin{bmatrix} x_0 \\ x_1 \\ \vdots \\ x_n \end{bmatrix}$ and $\vec{y} = \begin{bmatrix} y_0 \\ y_1 \\ \vdots \\ y_n \end{bmatrix}$ into a matrix

$$\begin{bmatrix}x_0 & y_0\\x_0 & y_1\\ \vdots & \vdots \\x_0 & y_m\\x_1 & y_0\\x_1 & y_1\\ \vdots & \vdots \\x_1 & y_m\\ \vdots & \vdots \\x_n & y_0 \\ x_n & y_1 \\ \vdots & \vdots \\ x_n & y_m\end{bmatrix} ?$$

How is this operation or this result called?

Answer 1

It's a block matrix $\begin{bmatrix}X& Y\end{bmatrix}$ of two columns $X=\vec x\otimes \vec 1_m$ and $Y=\vec1_n \otimes \vec y$, where $\vec 1$ is a vector of all ones, $\otimes$ is the Kronecker product.

Answer 2

I believe the phrase you want is 'augmented matrix'.