In this paper, we first give the representation of the general solution of the following inverse eigenvalue problem (IEP): <\/span>Given X ∈ Rn×p and a diagonal matrix Λ ∈ Rp×p, find <\/span>nontrivial real-valued symmetric arrow-head matrices A and B such <\/span>that AXΛ = BX. We then consider an optimal approximation <\/span>problem: Given real-valued symmetric arrow-head matrices A, ˜ B˜ ∈ <\/span>Rn×n, find (A, ˆ Bˆ) ∈ SE such that Aˆ − A˜2 + Bˆ − B˜2 = <\/span>min(A,B)∈SE (A−A˜2 +B −B˜2), where SE is the solution set <\/span>of IEP. We show that the optimal approximation solution (A, ˆ Bˆ) is <\/span>unique and derive an explicit formula for it.<\/span><\/p>\r\n", "references": null, "publisher": "World Academy of Science, Engineering and Technology", "index": "International Science Index 43, 2010" }