ON MATRIX INVERSE EIGENVALUE PROBLEMS

This paper discusses the matrix inverse eigenvalue problem: given matr ices C-0, C-1,..., C-n is an element of C-nxn, find scalars t = (t(1), ..., t(n)) is an element of C-n such that [GRAPHICS] has the prescribe d eigenvalues lambda(1),..., lambda(n). It is proven that this problem is equivalent to the joint eigenpair problem of a family of related m atrix pencils. Furthermore, the conditions under which this problem po ssesses a solution are given. A method for solving the joint eigenpair problem of a family of matrix pencils is then presented, which, in tu rn, gives all solutions of the problem. Some results in this paper may be of individual interest.