Solving the two-dimensional CIS problem by a rational algorithm - Al'pin, Yurii A.; George, Alan; Ikramov, Khakim D. (Linear algebra and its applications, 2000)
The CIS problem is formulated as follows. Let p be a fixed integer, 1⩽p<n. For given n×n compex matrices A and B, can one verify whether A and B have a common invariant subspace of dimension p by a procedure employing a finite number of arithmetical operations? We describe an algorithm solving the CIS problem for p=2. Unlike the algorithm proposed earlier by the second and third authors, the new algorithm does not impose any restrictions 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.