I am a new user to Mathematics forum. I would like to know if there is some simplification for expression $\sum\limits_{i,j = 1, \cdots, n} u_{ij} \alpha^i \beta^j$, and vector $u_{ij}$ cardinality is equal to $\lvert u_{ij} \rvert = n$.
I know, some expressions like element sum of Hadamard product $\sum\limits_{i,j} (A \circ B)_{ij} = \sum\limits_{i,j} A_{ij} B_{ij}$ as expression $\mbox{tr}(A B^\intercal) = \mbox{tr}(B A^\intercal)$
I thank you for your attention