KRONECKER BASES FOR LINEAR MATRIX EQUATIONS, WITH APPLICATION TO 2-PARAMETER EIGENVALUE PROBLEMS

The general solutions of the homogeneous matrix equation AXC(T) - BXD( T) = 0 and the system of the matrix equations AX + BY = 0, XC(T) + YDT = 0 are described in terms of Kronecker canonical forms, i.e., in ter ms of Kronecker invariants and Kronecker bases, for pairs of matrices (A, B) and (C, D). A canonical form for a pair of commuting matrices ( E, F) such that E(2) = F-2 = EF = 0 is discussed. These results are ap plied to construct a canonical basis for the second root subspace of a two-parameter eigenvalue problem. The corresponding relations for can onical invariants are given. (C) Elsevier Science Inc., 1996