A class of constrained inverse eigenvalue problem and associated approximation problem for symmetrizable matrices

Abstract

The real symmetric matrix is widely applied in various fields,
transforming non-symmetric matrix to symmetric matrix becomes very
important for solving the problems associated with the original
matrix. In this paper, we consider the constrained inverse eigenvalue problem
$AX=X\Lambda$ for the symmetrizable matrices, and obtain the solvability conditions and the general expression of the solution. Moreover, we consider the corresponding
optimal approximation problem, obtain the explicit expressions of the optimal approximation solution and
the minimum norm solution, and give the algorithm and corresponding computational
examples.