Solving the two-dimensional CIS problem by a rational algorithm (Q1573665)

The common invariant subspace (CIS) problem is discussed. Let \(1\leq p< n\) be a fixed integer, and \(A\) and \(B\) are complex matrices. Can one verify whether \(A\) and \(B\) have a common invariant subspace of dimension \(p\) in a finite number of steps? An algorithm is given which solves the problem for \(p=2\). No restrictions are imposed on \(A\) and \(B\). Moreover, when \(A\) and \(B\) generate a semisimple algebra, the algorithm is able to solve the CIS problem for any \(p, 1<p<n\).