<s>
is	O
a	O
matrix	B-Architecture
in	O
which	O
all	O
the	O
elements	O
are	O
equal	O
to	O
or	O
greater	O
than	O
zero	O
,	O
that	O
is	O
,	O
</s>
<s>
A	O
positive	B-Algorithm
matrix	I-Algorithm
is	O
a	O
matrix	B-Architecture
in	O
which	O
all	O
the	O
elements	O
are	O
strictly	O
greater	O
than	O
zero	O
.	O
</s>
<s>
While	O
such	O
matrices	O
are	O
commonly	O
found	O
,	O
the	O
term	O
is	O
only	O
occasionally	O
used	O
due	O
to	O
the	O
possible	O
confusion	O
with	O
positive-definite	B-Algorithm
matrices	I-Algorithm
,	O
which	O
are	O
different	O
.	O
</s>
<s>
A	O
matrix	B-Architecture
which	O
is	O
both	O
non-negative	O
and	O
is	O
positive	O
semidefinite	O
is	O
called	O
a	O
doubly	O
non-negative	B-Algorithm
matrix	I-Algorithm
.	O
</s>
<s>
A	O
rectangular	O
non-negative	B-Algorithm
matrix	I-Algorithm
can	O
be	O
approximated	O
by	O
a	O
decomposition	O
with	O
two	O
other	O
non-negative	O
matrices	O
via	O
non-negative	B-Algorithm
matrix	I-Algorithm
factorization	O
.	O
</s>
<s>
The	O
trace	O
and	O
every	O
row	O
and	O
column	O
sum/product	O
of	O
a	O
nonnegative	B-Algorithm
matrix	I-Algorithm
is	O
nonnegative	O
.	O
</s>
<s>
The	O
inverse	O
of	O
any	O
non-singular	O
M-matrix	B-Algorithm
is	O
a	O
non-negative	B-Algorithm
matrix	I-Algorithm
.	O
</s>
<s>
If	O
the	O
non-singular	O
M-matrix	B-Algorithm
is	O
also	O
symmetric	B-Algorithm
then	O
it	O
is	O
called	O
a	O
Stieltjes	O
matrix	B-Architecture
.	O
</s>
<s>
The	O
inverse	O
of	O
a	O
non-negative	B-Algorithm
matrix	I-Algorithm
is	O
usually	O
not	O
non-negative	O
.	O
</s>
<s>
The	O
exception	O
is	O
the	O
non-negative	O
monomial	B-Algorithm
matrices	I-Algorithm
:	O
a	O
non-negative	B-Algorithm
matrix	I-Algorithm
has	O
non-negative	O
inverse	O
if	O
and	O
only	O
if	O
it	O
is	O
a	O
(	O
non-negative	O
)	O
monomial	B-Algorithm
matrix	I-Algorithm
.	O
</s>
<s>
Note	O
that	O
thus	O
the	O
inverse	O
of	O
a	O
positive	B-Algorithm
matrix	I-Algorithm
is	O
not	O
positive	O
or	O
even	O
non-negative	O
,	O
as	O
positive	O
matrices	O
are	O
not	O
monomial	O
,	O
for	O
dimension	O
.	O
</s>
<s>
stochastic	B-Algorithm
matrix	I-Algorithm
;	O
doubly	B-Algorithm
stochastic	I-Algorithm
matrix	I-Algorithm
;	O
symmetric	B-Algorithm
non-negative	B-Algorithm
matrix	I-Algorithm
.	O
</s>
