The inverse eigenvalue problem for a Hermitian reflexive matrix and the optimization problem

The inverse eigenvalue problem and the associated optimal approximation problem for Hermitian reflexive matrices with respect to a normal {k+1}-potent matrix are considered. First, we study the existence of the solutions of the associated inverse eigenvalue problem and present an explicit form for them. Then, when such a solution exists, an expression for the solution to the corresponding optimal approximation problem is obtained.This work was partially supported by Ministerio de Economia y Competitividad (DGI Grant MTM2013-43678-P) and by Universidad de Buenos Aires (20020130100671BA, EXP-UBA: 9.011/2013).Gigola, SV.; Lebtahi Ep-Kadi-Hahifi, L.; Thome, N. (2016). The inverse eigenvalue problem for a Hermitian reflexive matrix and the optimization problem. Journal of Computational and Applied Mathematics. 291:449-457. https://doi.org/10.1016/j.cam.2015.03.05244945729