<s>
In	O
mathematics	O
,	O
the	O
Redheffer	B-Algorithm
star	I-Algorithm
product	I-Algorithm
is	O
a	O
binary	O
operation	O
on	O
linear	B-Architecture
operators	I-Architecture
that	O
arises	O
in	O
connection	O
to	O
solving	O
coupled	O
systems	O
of	O
linear	O
equations	O
.	O
</s>
<s>
Given	O
two	O
scattering	O
matrices	O
from	O
different	O
linear	O
scatterers	O
,	O
the	O
Redheffer	B-Algorithm
star	I-Algorithm
product	I-Algorithm
yields	O
the	O
combined	O
scattering	O
matrix	O
produced	O
when	O
some	O
or	O
all	O
of	O
the	O
output	O
channels	O
of	O
one	O
scatterer	O
are	O
connected	O
to	O
inputs	O
of	O
another	O
scatterer	O
.	O
</s>
<s>
The	O
Redheffer	B-Algorithm
star	I-Algorithm
product	I-Algorithm
is	O
then	O
defined	O
by	O
:	O
</s>
<s>
linear	B-Architecture
operators	I-Architecture
on	O
a	O
Hilbert	O
space	O
.	O
</s>
<s>
Thus	O
when	O
either	O
exists	O
,	O
so	O
does	O
the	O
Redheffer	B-Algorithm
star	I-Algorithm
product	I-Algorithm
.	O
</s>
<s>
The	O
Redheffer	B-Algorithm
star	I-Algorithm
product	I-Algorithm
can	O
be	O
used	O
to	O
solve	O
for	O
the	O
propagation	O
of	O
electromagnetic	O
fields	O
in	O
stratified	O
,	O
multilayered	O
media	O
.	O
</s>
