Normal forms of regular matrix polynomials via local rank factorization

The `local rank factorization' (lrf) of a regular matrix polynomial at an eigenvalue consists of a sequence of matrix rank factorizations of a certain function of its coecients; the lrf delivers the local Smith form and extended canonical systems of root functions that correspond to the eigenvalue. In this paper it is shown that by performing the lrf at each finite eigenvalue and at infinity one can contruct the Smith form, Jordan triples and decomposable pairs of the matrix polynomial. When A(l) = A-lB, where A,B belong to C(pxp), the analysis delivers the Kronecker form of A(l) and strict similarity transformations; for B = I one finds the Jordan form of A and Jordan bases.