On solvability of inverse eigenvalue problems with Hermitian matrices (Q677124)

Let \(A,A_1 ,\dots ,A_n\) be given Hermitian \(n\times n\) matrices, where the \(i\)th diagonal element of \(A_t\) is \(\delta _{it}\), and let \(\lambda _1 ,\dots , \lambda _n\) be distinct real numbers. The author establishes some sufficient conditions for the existence of real numbers \(c_1 ,\dots ,c_n\) such that \(A+\sum_{t=1}^n c_t A_t\) has eigenvalues \(\lambda _1 ,\dots , \lambda _n\). Some additional results are proved for the multiplicative inverse eigenvalue problem.