A simple and constructive proof is given for the existence of a real symmetric matrix with prescribed diagonal elements and eigenvalues. Numerically implementable algorithms for constructing such a matrix are discussed. © 1983.
Chan, N. N., & Li, K. H. (1983). Diagonal elements and eigenvalues of a real symmetric matrix. Journal of Mathematical Analysis and Applications, 91(2), 562–566. https://doi.org/10.1016/0022-247X(83)90171-3