<s>
In	O
mathematics	O
,	O
a	O
moment	B-Algorithm
matrix	I-Algorithm
is	O
a	O
special	O
symmetric	O
square	O
matrix	B-Architecture
whose	O
rows	O
and	O
columns	O
are	O
indexed	O
by	O
monomials	O
.	O
</s>
<s>
The	O
entries	O
of	O
the	O
matrix	B-Architecture
depend	O
on	O
the	O
product	O
of	O
the	O
indexing	O
monomials	O
only	O
(	O
cf	O
.	O
</s>
<s>
Hankel	B-Algorithm
matrices	I-Algorithm
.	O
)	O
</s>
<s>
Moment	O
matrices	O
play	O
an	O
important	O
role	O
in	O
polynomial	O
fitting	O
,	O
polynomial	O
optimization	O
(	O
since	O
positive	B-Algorithm
semidefinite	I-Algorithm
moment	O
matrices	O
correspond	O
to	O
polynomials	O
which	O
are	O
sums	O
of	O
squares	O
)	O
and	O
econometrics	O
.	O
</s>
<s>
Given	O
observations	O
,	O
we	O
have	O
a	O
system	O
of	O
linear	O
equations	O
that	O
can	O
be	O
expressed	O
in	O
matrix	B-Architecture
notation	O
.	O
</s>
<s>
where	O
and	O
are	O
each	O
a	O
vector	O
of	O
dimension	O
,	O
is	O
the	O
design	B-Algorithm
matrix	I-Algorithm
of	O
order	O
,	O
and	O
is	O
a	O
vector	O
of	O
dimension	O
.	O
</s>
<s>
where	O
is	O
a	O
square	O
normal	B-Algorithm
matrix	I-Algorithm
of	O
dimension	O
,	O
and	O
is	O
a	O
vector	O
of	O
dimension	O
.	O
</s>
