English

How to solve three fundamental linear matrix inequalities in the L\"owner partial ordering

Optimization and Control 2013-01-30 v1 Systems and Control Operator Algebras

Abstract

This paper shows how to solve analytically the three fundamental linear matrix inequalities AXBC(C),  AXAB(B),  AX+(AX)B(B) AXB \succcurlyeq C \, (\succ C), \ \ AXA^*\succcurlyeq B \, (\succ B), \ \ AX +(AX)^{*} \succcurlyeq B \, (\succ B) in the L\"owner partial ordering by using ranks, inertias and generalized inverses of matrices.

Keywords

Cite

@article{arxiv.1301.6752,
  title  = {How to solve three fundamental linear matrix inequalities in the L\"owner partial ordering},
  author = {Yongge Tian},
  journal= {arXiv preprint arXiv:1301.6752},
  year   = {2013}
}

Comments

37 pages