A note on the minimal polynomial of the Kronecker sum of two linear operators (Q921081)

Let \(f\), \(g\) denote linear transformations on finite dimensional vector spaces \(V\), \(W\) respectively, and let \(I\) denote an identity operator (on \(V\) or \(W\) as determined by the context). The Kronecker sum of \(f\) and \(g\) is \(f\otimes I+I\otimes g\). The authors give a lower bound for the degree of the minimal polynomial of the Kronecker sum of \(f\) and \(g\) in terms of the degrees of the minimal polynomial of \(f\) and \(g\).