<s>
In	O
mathematics	O
,	O
a	O
Bézout	B-Algorithm
matrix	I-Algorithm
(	O
or	O
Bézoutian	O
or	O
Bezoutiant	B-Algorithm
)	O
is	O
a	O
special	O
square	B-Algorithm
matrix	I-Algorithm
associated	O
with	O
two	O
polynomials	O
,	O
introduced	O
by	O
and	O
and	O
named	O
after	O
Étienne	O
Bézout	O
.	O
</s>
<s>
To	O
each	O
Bézout	B-Algorithm
matrix	I-Algorithm
,	O
one	O
can	O
associate	O
the	O
following	O
bilinear	O
form	O
,	O
called	O
the	O
Bézoutian	O
:	O
</s>
<s>
is	O
symmetric	B-Algorithm
(	O
as	O
a	O
matrix	O
)	O
;	O
</s>
<s>
f	O
is	O
Hurwitz	O
stable	O
if	O
and	O
only	O
if	O
is	O
positive	B-Algorithm
definite	I-Algorithm
.	O
</s>
<s>
Besides	O
,	O
the	O
first	O
statement	O
exhibits	O
some	O
similarities	O
with	O
a	O
result	O
concerning	O
Sylvester	B-Algorithm
matrices	I-Algorithm
while	O
the	O
second	O
one	O
can	O
be	O
related	O
to	O
Routh	O
–	O
Hurwitz	O
theorem	O
.	O
</s>
