Talk : A theorem about linear inequalities with an application (Prof. K.N.Raghavan – IMSc)

Talk On 17th  February  2016 , at 2.15p.m.
Title    :    A theorem about linear inequalities with an application.
Speaker: Prof.K.N.Raghavan, Institute of Mathematical Sciences(IMSc),Chennai
Venue: Auditorium , Dept.Of Mathematics
COCHIN UNIVERSITY OF SCIENCE & TECHNOLOGY

Abstract:

Let B be a m x n real matrix and B’ be its transpose.    Suppose that this holds:  if B’v>=0 and v>=0 then v=0.     Then there exists a solution to the equation Bx>0.        We will apply this result to classify “indecomposable” real square matrices satisfying these properties:  (i) the non-diagonal entries are non-negative, and (ii) if the entry in position (i,j) is zero,  then so is the one in position (j,i).     “Indecomposable” just means that the matrix cannot be written as a direct sum in the obvious sense of two such matrices of smaller size.      This classification is important in the theory of infinite dimensional Lie algebras,  but should be interesting in its own right.