Polynomial similarity of pairs of matrices

Vitaliy Bondarenko, Anatoliy Petravchuk, Maryna Styopochkina

Let $K$ be a field, $R=K[x,y]$ the polynomial ring and $\mathcal{M}(K)$ the set of all pairs of square matrices of the same size over $K.$ Pairs $P_1=(A_1,B_1)$ and $P_2=(A_2,B_2)…