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.