RUTCOR Colloquium:
Speaker: Alan J. Hoffman (
Heights, NY)
Abstract: GERSGORIN VARIATIONS
Gersgorin's theorem (equivalenty, Desplanques theorem)
says that a
matrix where, in each row, the
modulus of the diagonal entry exceeds the sum of
the moduli
of the other entries, is nonsingular.
There are many generalizations of this theorem. We will
discuss their
general flavor, and (in more
detail) recent results of Boros, Brualdi,
Crama and Hoffman.
These depend heavily (as well they should!) on methods of
linear
programming. There is also a connection to Jacobi (!), as pointed out
by Prof. Cohn of the Mathematics
Dept.