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

Yongge Tian

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arXiv · 1301.6752

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

Yongge Tian

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Abstract

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

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Yongge Tian. 2013-01-28. How to solve three fundamental linear matrix inequalities in the L\"owner partial ordering. https://arxiv.org/abs/1301.6752

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