I have a matrix $\boldsymbol{N}$ and a vector $\boldsymbol{u}$. The vector $\boldsymbol{u}$ contains column indices of $\boldsymbol{N}$, and they both have $m$ rows. I would like to define an recursive algorithm that is (conceptually) something like this: $$\boldsymbol{N}_{n+1}=\boldsymbol{N}_n+\sum_{i=1}^{m}\boldsymbol{N}_{i*}\otimes\boldsymbol{N}_{*\boldsymbol{u}_i}$$
Where $\boldsymbol{N}$ on the right side of the equal sign reffers $\boldsymbol{N}_n$. However, because I am using index notation, this becomes confusing. I use index notation extensively everywhere else in my paper. How should I denote this concept?