ABSTRACT
In general, an inverse eigenvalue problem (IEP) consists of the construction of a matrix with prescribed structural and spectral constraints. This is a two-level problem: (1) on a theoretical level the target is to determine if the IEP is solvable, that is, to find necessary and sufficient conditions for the existence of at least one solution matrix (a matrix with the given constraints); and (2) on a practical level, the target is the effective construction of a solution matrix when the IEP is solvable. IEPs are classified into different types according to the specific constraints. We will consider three topics: IEPs with prescribed entries, nonnegative IEPs, and affine parameterized IEPs. Other important topics include pole assignment problems, Jacobi IEPs, inverse singular value problems, etc. For interested readers, we refer to the survey [CG02] where an account of IEPs with applications and extensive bibliography can be found.
