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On matrix inverse eigenvalue problems

Xingzhi Ji

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This paper discusses the matrix inverse eigenvalue problem: given matrices , find scalars such that

has the prescribed eigenvalues . It is proven that this problem is equivalent to the joint eigenpair problem of a family of related matrix pencils. Furthermore, the conditions under which this problem possesses a solution are given. A method for solving the joint eigenpair problem of a family of matrix pencils is then presented, which, in turn, gives all solutions of the problem. Some results in this paper may be of individual interest.


PACS

02.30.Zz Inverse problems

02.10.Yn Matrix theory

02.10.Ud Linear algebra

MSC

15A18 Eigenvalues, singular values, and eigenvectors

15A29 Inverse problems

Subjects

Mathematical physics

Dates

Issue 2 (April 1998)

Received 24 June 1996, in final form 28 August 1997



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