Adjoint matrix, Bezout theorem, Cayley-Hamilton theorem, and Fadeev's method for the matrix pencil(sE-A)

The use of the, adjoint matrix for finding eigenvectors, the Bezout theorem, the Cayley-Hamilton theorem, Fadeev's method, and other results are generalized to the case of a regular matrix pencil (sE-A) where E and A may both in general be singular. The notion of minor of A relative to E is introduced to study the interactions of the two matrices.