Decomposition of a matrix pencil into linear factors (Q1814463)

The author considers the problem of factorization of matrix pencils of the form \[ L(\lambda)=A_ 0+\lambda A_ 1+\lambda^ 2 A_ 2+\dots+\lambda^ n A_ n,\qquad \det A_ n\neq 0, \] into the product of linear factors. The main result is the following. If degrees of all primary divisors of \(L\) are less or equal to 2, then there is a required factorization.