Generic canonical form of pairs of matrices with zeros. (Q1428625)

The authors consider a family of pairs of matrices, in which some entries are required to be zero and the others are arbitrary, with respect to transformations \((A, B)\mapsto(SAR_1,SBR_2)\) with nonsingular \(S\), \(R_1\), and \(R_2\). The authors prove that almost all of these pairs reduce to the same pair \((A_0,B_0)\) from this family. Section 1 contains two theorems as main results of this paper. Section 2 presents the proofs of these two theorems.