A Fresh Variational-Analysis Look at the Positive Semidefinite Matrices World

@article{HiriartUrruty2012AFV,
  title={A Fresh Variational-Analysis Look at the Positive Semidefinite Matrices World},
  author={Jean-Baptiste Hiriart-Urruty and J{\'e}r{\^o}me Malick},
  journal={J. Optimization Theory and Applications},
  year={2012},
  volume={153},
  pages={551-577}
}
Engineering sciences and applications of mathematics show unambiguously that positive semidefiniteness of matrices is the most important generalization of non-negative real numbers. This notion of non-negativity for matrices has been well-studied in the literature; it has been the subject of review papers and entire chapters of books. This paper reviews some of the nice, useful properties of positive (semi)definite matrices, and insists in particular on (i) characterizations of positive (semi… CONTINUE READING