English

Inequalities with Determinants of Perturbed Positive Matrices

Rings and Algebras 2014-02-17 v1

Abstract

We prove two inequalities regarding the ratio det(A+D)/detA\det(A+D)/\det A of the determinant of a positive-definite matrix AA and the determinant of its perturbation A+DA+D. In the first problem, we study the perturbations that happen when positive matrices are added to diagonal blocks of the original matrix. In the second problem, the perturbations are added to the inverses of the matrices.

Keywords

Cite

@article{arxiv.1402.3548,
  title  = {Inequalities with Determinants of Perturbed Positive Matrices},
  author = {Ivan Matic},
  journal= {arXiv preprint arXiv:1402.3548},
  year   = {2014}
}