<s>
The	O
Plücker	B-Algorithm
matrix	I-Algorithm
is	O
a	O
special	O
skew-symmetric	B-Algorithm
44	O
matrix	B-Architecture
,	O
which	O
characterizes	O
a	O
straight	O
line	O
in	O
projective	O
space	O
.	O
</s>
<s>
The	O
matrix	B-Architecture
is	O
defined	O
by	O
6	O
Plücker	O
coordinates	O
with	O
4	O
degrees	O
of	O
freedom	O
.	O
</s>
<s>
Its	O
Plücker	B-Algorithm
matrix	I-Algorithm
is	O
:	O
</s>
<s>
A	O
Plücker	B-Algorithm
matrix	I-Algorithm
has	O
only	O
rank2	O
and	O
four	O
degrees	O
of	O
freedom	O
(	O
just	O
like	O
lines	O
in	O
)	O
.	O
</s>
<s>
The	O
Plücker	B-Algorithm
matrix	I-Algorithm
allows	O
us	O
to	O
express	O
the	O
following	O
geometric	O
operations	O
as	O
matrix-vector	O
product	O
:	O
</s>
<s>
Their	O
Plücker	B-Algorithm
matrix	I-Algorithm
is	O
thus	O
:	O
</s>
<s>
In	O
addition	O
,	O
the	O
product	O
of	O
the	O
Plücker	B-Algorithm
matrix	I-Algorithm
with	O
a	O
plane	O
is	O
the	O
zero-vector	O
,	O
exactly	O
if	O
the	O
line	O
is	O
contained	O
entirely	O
in	O
the	O
plane	O
:	O
</s>
<s>
In	O
case	O
of	O
the	O
Plücker	B-Algorithm
matrix	I-Algorithm
,	O
there	O
exists	O
a	O
dual	O
representation	O
of	O
the	O
line	O
in	O
space	O
as	O
the	O
intersection	O
of	O
two	O
planes	O
:	O
</s>
<s>
Their	O
Plücker	B-Algorithm
matrix	I-Algorithm
is	O
:	O
</s>
<s>
The	O
relationship	O
to	O
Plücker	O
matrices	O
becomes	O
evident	O
,	O
if	O
one	O
writes	O
the	O
cross	O
product	O
as	O
a	O
matrix-vector	O
product	O
with	O
a	O
skew-symmetric	B-Algorithm
matrix	I-Algorithm
:	O
</s>
