Talk:Linear matrix inequality

This page needs cleanup. The convexity discussion is not needed in my opinion, also references to freely unavailable sources should be minimized. nszabolcs 09:02, 5 October 2007 (UTC)


 * The author notes "This linear matrix inequality specifies a convex constraint on y." The shape of that set is not at all obvious.  Secondly, does this LMI definition stand on its own?  What are its origins?  That is why the convexity discussion is warranted, in my opinion.  --Dattorro 10:31, 5 October 2007 (UTC)


 * I prefer a clean minimalistic definition which is correct. Lengthy, technical proofs makes the article messed also new notations and concepts makes it harder to follow. The shape is not obvious, but it's important to mention that it's convex (probably a note should be added there about convexity discussion?). Anyway if the current definition is ok and the cited references contain enough detailed information then i'd leave the article this way. Those who are interested will read the references anyway. nszabolcs 16:03, 23 October 2007 (UTC)

What is meant by an inequality applied to a matrix?
This article does not address what is meant by A >= 0. Is every value in A greater than zero, or is there something more to it than that? I think this issue should be addressed in this page, as this is the Wikipedia article that pops up when matrix inequality is searched in Google. — Preceding unsigned comment added by OceanEngineerRI (talk • contribs) 01:53, 19 October 2012 (UTC)

The definition is not correct.
Given LMI on this post is a quite particular LMI and shows up only in parametrizing them. Sign definiteness comes after the the definition which is the other way around. This is not minimalistic but unfortunately misleading. Convexity of the semidefinite cone is not related to LMIs per se. And the term is coined in J.C. Willems "Least squares stationary optimal control and the algebraic Riccati equation" DOI : 10.1109/TAC.1971.1099831. Moreover, in the current definition due to the $A_0$ term it is widely known that it should have been called an affine matrix inequality etc. If needed one should start from the Löwner partial ordering and then define what $>$ operation means otherwise I agree with the previous commenter it's not addressed though crucial. — Preceding unsigned comment added by 2001:980:D4FB:1:B430:DCAF:A4FB:17CA (talk) 12:08, 26 December 2012 (UTC)