This article concerns the question: which subsets of R can be represented with Linear Matrix Inequalities, LMIs? This gives some perspective on the scope and limitations of one of the most powerful techniques commonly used in control theory. Also before having much hope of representing engineering problems as LMIs by automatic methods one needs a good idea of which problems can and cannot be re...

Convention: Let A be a T×m matrix; the notation vec(A) will mean the Tmelement column vector whose first set of T elements are the first colum of A, that is a.1 using the dot notation for columns; the second set of T elements are those of the second column of A, a.2, and so on. Thus A = [a.1, a.2, · · · , a.m] in the dot notation. An immediate consequences of the above Convention is Vec of a pr...

1. An O(mm(n) log(n)) = O(nω+ ) algorithm which finds the shortest distance matrix for a graph G by recursively finding the shortest distance matrix for the graph G2. 2. The problem of determining the successor matrix for tripartite graphs. 3. O(nω) time algorithm for finding successor matrix in in a simple tripartite graph when there is a unique successor for any 2 vertices. 4. An O(mm(n) log(...