Constructing a Hermitian Matrix from Its Diagonal Entries and Eigenvalues

@article{Chu1995ConstructingAH,
  title={Constructing a Hermitian Matrix from Its Diagonal Entries and Eigenvalues},
  author={Moody T. Chu},
  journal={SIAM J. Matrix Analysis Applications},
  year={1995},
  volume={16},
  pages={207-217}
}
Given two vectors a; 2 Rn, the Schur-Horn theorem states that a majorizes if and only if there exists a Hermitian matrix H with eigenvalues and diagonal entries a. While the theory is regarded as classical by now, the known proof is not constructive. To construct a Hermitian matrix from its diagonal entries and eigenvalues therefore becomes an interesting and challenging inverse eigenvalue problem. Two algorithms for determining the matrix numerically are proposed in this paper. The lift and… CONTINUE READING

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