I have a matrix of the form,
$$ \begin{bmatrix} x_1^\top A x_1, \ldots, x_1^\top A x_n \\ \cdots, \cdots, \cdots, \\ x_m^\top A x_1, \ldots, x_m^\top A x_n \end{bmatrix} $$
where $A$ is some matrix, and $x_i$'s are column vectors with the appropriate dimensions for the matrix $A$. Note that each element of the above matrix is a scalar in the quadratic form $x_i^\top A x_j$.
Question: Is there a nice compact notation to express the above?
I thought about using Kronecker product; say $B \otimes C $ has elements that look like $b_{ij} C$, which is close to what I'm looking for, except that I have a scalar $b_{ij}$ multiplying the matrix $C$ instead of a vector-times-matrix product.
Thanks!