Author’s summary: This paper discusses the inverse eigenvalue least squares problem: Given an \(n\times n\) matrix \(A^*\), an \(n\times k\) matrix X and a \(k\times k\) diagonal matrix \(\Lambda\), find an \(n\times n\) matrix A minimizing \(\| AX-X\Lambda \|_ F\) and \(\| A^*- A\|_ F\). An expression and a perturbation analysis of the solution to this problem are given, numerical methods are described, numerical experiments are included and a class of ill-conditioned problems is considered.