Thursday, January 25, 2018 1:30 pm
-
1:30 pm
EST (GMT -05:00)
Title: Type-II Matrices
| Speaker | Chris Godsil |
| Affiliation: | University of Waterloo |
| Room | MC 6486 |
Abstract:
The
Schur
product
M
o
N
of
two
matrices
M
and
N
is
the
usual
entrywise
product.
The
matrix
N
is
the
Schur
inverse
of
M
if
M
o
N
=
J.
Denote
the
Schur
inverse
of
M
by
M(-).
An
n
x
n matrix
is
a
type-II
matrix
if
WW(-)T
=
nI.
(Thus
the
usual
inverse
can
be
read
from
the
Schur
inverse.)
Hadamard
matrices
provide
one
class
of
type-II
matrices,
but
they
occur
in
a
surprising
range
of
places.
I
will
discuss
some
of
the
basic
properties
of
type-II
matrices,
and
their
connection
with
interesting
objects
such
as
symmetric
designs
and
magic
unitary
matrices.