<s>
In	O
mathematics	O
,	O
the	O
class	O
of	O
Z-matrices	O
are	O
those	O
matrices	B-Architecture
whose	O
off-diagonal	O
entries	O
are	O
less	O
than	O
or	O
equal	O
to	O
zero	O
;	O
that	O
is	O
,	O
the	O
matrices	B-Architecture
of	O
the	O
form	O
:	O
</s>
<s>
Note	O
that	O
this	O
definition	O
coincides	O
precisely	O
with	O
that	O
of	O
a	O
negated	O
Metzler	B-Algorithm
matrix	I-Algorithm
or	O
quasipositive	B-Algorithm
matrix	I-Algorithm
,	O
thus	O
the	O
term	O
quasinegative	O
matrix	O
appears	O
from	O
time	O
to	O
time	O
in	O
the	O
literature	O
,	O
though	O
this	O
is	O
rare	O
and	O
usually	O
only	O
in	O
contexts	O
where	O
references	O
to	O
quasipositive	O
matrices	B-Architecture
are	O
made	O
.	O
</s>
<s>
The	O
Jacobian	O
of	O
a	O
competitive	O
dynamical	O
system	O
is	O
a	O
Z-matrix	B-Algorithm
by	O
definition	O
.	O
</s>
<s>
Likewise	O
,	O
if	O
the	O
Jacobian	O
of	O
a	O
cooperative	O
dynamical	O
system	O
is	O
J	O
,	O
then	O
(	O
J	O
)	O
is	O
a	O
Z-matrix	B-Algorithm
.	O
</s>
<s>
Related	O
classes	O
are	O
L-matrices	B-Algorithm
,	O
M-matrices	B-Algorithm
,	O
P-matrices	O
,	O
Hurwitz	B-Algorithm
matrices	I-Algorithm
and	O
Metzler	O
matrices	B-Architecture
.	O
</s>
<s>
L-matrices	B-Algorithm
have	O
the	O
additional	O
property	O
that	O
all	O
diagonal	O
entries	O
are	O
greater	O
than	O
zero	O
.	O
</s>
<s>
M-matrices	B-Algorithm
have	O
several	O
equivalent	O
definitions	O
,	O
one	O
of	O
which	O
is	O
as	O
follows	O
:	O
a	O
Z-matrix	B-Algorithm
is	O
an	O
M-matrix	B-Algorithm
if	O
it	O
is	O
nonsingular	O
and	O
its	O
inverse	O
is	O
nonnegative	O
.	O
</s>
<s>
All	O
matrices	B-Architecture
that	O
are	O
both	O
Z-matrices	O
and	O
P-matrices	O
are	O
nonsingular	O
M-matrices	B-Algorithm
.	O
</s>
<s>
In	O
the	O
context	O
of	O
quantum	O
complexity	O
theory	O
,	O
these	O
are	O
referred	O
to	O
as	O
stoquastic	B-Algorithm
operators	O
.	O
</s>
