I have a construction on two vector bundles and I would like to give it a name and a symbol but I can't find anything.

For two vector bundles $A=\{(x,A_x) : x \in X\}$ and $B=\{(y,B_y):y\in Y\}$ there is a vector bundle on $X\times Y$:

$$ A \mathop{?} B = \{((x,y),\text{L}(A_x,B_y)) : (x,A_x) \in A, (y,B_y) \in B\} $$

$\text{L}(V,W)$ denotes the linear mappings from $V$ to $W$.

Does anyone know this construction? Has it a name?

For $X = Y$ I know the Hom bundle but this would be a vector bundle on $X$ instead of $X^2$ and this makes it incompatible with the construction above.

References appreciated, thanks!

imix