The purpose of this document is to collect and organize properties, tricks,
and applications related to linear matrix inequalities (LMIs) from a number of
references together in a single document. Proofs of the properties presented in
this document are not included when they can be found in the cited references
in the interest of brevity. Illustrative examples are included whenever
necessary to fully explain a certain property. Multiple equivalent forms of
LMIs are often presented to give the reader a choice of which form may be best
suited for a particular problem at hand. The equivalency of some of the LMIs in
this document may be straightforward to more experienced readers, but the
authors believe that some readers may benefit from the presentation of multiple
equivalent LMIs.