<s>
In	O
mathematics	O
,	O
particularly	O
linear	B-Language
algebra	I-Language
,	O
a	O
zero	B-Algorithm
matrix	I-Algorithm
or	O
null	B-Algorithm
matrix	I-Algorithm
is	O
a	O
matrix	B-Architecture
all	O
of	O
whose	O
entries	O
are	O
zero	O
.	O
</s>
<s>
It	O
also	O
serves	O
as	O
the	O
additive	O
identity	O
of	O
the	O
additive	O
group	O
of	O
matrices	O
,	O
and	O
is	O
denoted	O
by	O
the	O
symbol	O
or	O
followed	O
by	O
subscripts	O
corresponding	O
to	O
the	O
dimension	O
of	O
the	O
matrix	B-Architecture
as	O
the	O
context	O
sees	O
fit	O
.	O
</s>
<s>
The	O
zero	B-Algorithm
matrix	I-Algorithm
in	O
is	O
the	O
matrix	B-Architecture
with	O
all	O
entries	O
equal	O
to	O
,	O
where	O
is	O
the	O
additive	O
identity	O
in	O
K	O
.	O
</s>
<s>
The	O
zero	B-Algorithm
matrix	I-Algorithm
is	O
the	O
additive	O
identity	O
in	O
.	O
</s>
<s>
There	O
is	O
exactly	O
one	O
zero	B-Algorithm
matrix	I-Algorithm
of	O
any	O
given	O
dimension	O
mn	O
(	O
with	O
entries	O
from	O
a	O
given	O
ring	O
)	O
,	O
so	O
when	O
the	O
context	O
is	O
clear	O
,	O
one	O
often	O
refers	O
to	O
the	O
zero	B-Algorithm
matrix	I-Algorithm
.	O
</s>
<s>
The	O
zero	B-Algorithm
matrix	I-Algorithm
also	O
represents	O
the	O
linear	B-Architecture
transformation	I-Architecture
which	O
sends	O
all	O
the	O
vectors	O
to	O
the	O
zero	O
vector	O
.	O
</s>
<s>
The	O
zero	B-Algorithm
matrix	I-Algorithm
is	O
the	O
only	O
matrix	B-Architecture
whose	O
rank	O
is	O
0	O
.	O
</s>
<s>
The	O
mortal	O
matrix	B-Architecture
problem	O
is	O
the	O
problem	O
of	O
determining	O
,	O
given	O
a	O
finite	O
set	O
of	O
n	O
×	O
n	O
matrices	O
with	O
integer	O
entries	O
,	O
whether	O
they	O
can	O
be	O
multiplied	O
in	O
some	O
order	O
,	O
possibly	O
with	O
repetition	O
,	O
to	O
yield	O
the	O
zero	B-Algorithm
matrix	I-Algorithm
.	O
</s>
<s>
In	O
ordinary	B-General_Concept
least	I-General_Concept
squares	I-General_Concept
regression	I-General_Concept
,	O
if	O
there	O
is	O
a	O
perfect	O
fit	O
to	O
the	O
data	O
,	O
the	O
annihilator	O
matrix	B-Architecture
is	O
the	O
zero	B-Algorithm
matrix	I-Algorithm
.	O
</s>
