Characteristic Polynomial in Several Variables

For a square matrix \(A\in M_k({\mathbb C})\) , its characteristic polynomial \(Q_A(z)=\det (z-A)\) is a basic subject of study in linear algebra. The idea of connecting a matrix with a polynomial has far-reaching impact in many ways. However, studies in mathematics, science, technology, and engineering often concern with several matrices \(A_1, \dots , A_n\) with algebraic connections.