I sincerely hope this question is interesting for you to answer.
Assume that $V\in\mathbb{R}^{1\times k}$, $B_i\in\mathbb{R}^{k\times 1}$, $T_i\in\mathbb{R}^{k\times k}$ with $i=1\dots k$, and, finally $L\in\mathbb{R}^{1\times k}$. I've the following equation to solve for V (all other matrices are assumed to be known):
$$\begin{equation} V - VB_1VT_1 - VB_2VT_2 - \dots - VB_kVT_k = L\end{equation}$$
I would like to know if such an equation can be classified as a particular equation with known solution, for example, a Sylvester equation (I know that the proposed equation is nonlinear though), or any other type, such that the solution can be found in a closed-form expression.
Thanks!!!!
