<s>
In	O
mathematics	O
,	O
a	O
Hurwitz	B-Algorithm
matrix	I-Algorithm
,	O
or	O
Routh	O
–	O
Hurwitz	B-Algorithm
matrix	I-Algorithm
,	O
in	O
engineering	O
stability	B-Algorithm
matrix	I-Algorithm
,	O
is	O
a	O
structured	O
real	B-Algorithm
square	I-Algorithm
matrix	I-Algorithm
constructed	O
with	O
coefficients	O
of	O
a	O
real	O
polynomial	O
.	O
</s>
<s>
is	O
called	O
Hurwitz	B-Algorithm
matrix	I-Algorithm
corresponding	O
to	O
the	O
polynomial	O
.	O
</s>
<s>
In	O
engineering	O
and	O
stability	O
theory	O
,	O
a	O
square	B-Algorithm
matrix	I-Algorithm
is	O
called	O
a	O
stable	O
matrix	O
(	O
or	O
sometimes	O
a	O
Hurwitz	B-Algorithm
matrix	I-Algorithm
)	O
if	O
every	O
eigenvalue	O
of	O
has	O
strictly	O
negative	O
real	O
part	O
,	O
that	O
is	O
,	O
</s>
<s>
Note	O
that	O
it	O
is	O
not	O
necessary	O
that	O
for	O
a	O
specific	O
argument	O
be	O
a	O
Hurwitz	B-Algorithm
matrix	I-Algorithm
—	O
it	O
need	O
not	O
even	O
be	O
square	O
.	O
</s>
<s>
The	O
Hurwitz	O
stability	B-Algorithm
matrix	I-Algorithm
is	O
a	O
crucial	O
part	O
of	O
control	O
theory	O
.	O
</s>
<s>
A	O
system	O
is	O
stable	O
if	O
its	O
control	O
matrix	O
is	O
a	O
Hurwitz	B-Algorithm
matrix	I-Algorithm
.	O
</s>
