In this paper, the infinite eigenvalue assignment problem for singular systems is studied. Necessary and sufficient conditions are presented under which there exists a state feedback such that the closed-loop system is regular and has only infinite eigenv

Given an arbitrary commutative field K, image and two monic polynomials q and r over K of degree n−1 and n such that q(0)≠0≠r(0). We prove that any non-scalar invertible n×n matrix M can be written as a product of two matrices A and B, where the minimum polynomial of A is divisible by q and B is cyclic with minimum polynomial r. This result yields that the Thompson conjecture is true for PSLn(F3), image , and PSL2n+1(F2), image . If G is such a group, then G has a conjugacy class Ω such that G=Ω2. In particular each element of G is a commutator.