Write summation of vector outer products into matrix form

Question

My question is as follows:

Given the weighted summation of vector outer products $\sum_i\sum_jh_{ij}{\bf v_i}{\bf u_j}^T$, where $h_{ij}$ is the weight, and ${\bf v_i,u_j}$ are column vectors, I was wondering if we could write it in a more elegant matrix form?

For example, a simpler case $\sum_i {\bf u_i}{\bf u_i}^T$, we can write it in the matrix form ${\bf UU}^T$, where ${\bf U}=[{\bf u_1,u_2},\ldots]$.

Thanks!

Answer 1

How about

$$VHU^T$$

where $U=[u_1,u_2,\ldots,u_n]$, $V=[v_1,v_2,\ldots,v_n]$ and $H=[h_{ij}]$.