Let $M$ be a square matrix of size $n$, $(a_i)_{i\in[1,n]},(b_i)_{i\in[1,n]},y$ vectors of size $n$ and $\lambda$ a real.
Is there a closed form for the following problem:
$$\arg\min_M \sum_i(y_i-a_i^TMb_i)^2+\lambda||M||^2_2$$
Where $||M||^2_2$ is the sum of squares of the elements of the matrix.