<s>
In	O
the	O
mathematical	O
field	O
of	O
linear	B-Language
algebra	I-Language
,	O
an	O
arrowhead	B-Algorithm
matrix	I-Algorithm
is	O
a	O
square	B-Algorithm
matrix	I-Algorithm
containing	O
zeros	O
in	O
all	O
entries	O
except	O
for	O
the	O
first	O
row	O
,	O
first	O
column	O
,	O
and	O
main	O
diagonal	O
,	O
these	O
entries	O
can	O
be	O
any	O
number	O
.	O
</s>
<s>
Any	O
symmetric	O
permutation	O
of	O
the	O
arrowhead	B-Algorithm
matrix	I-Algorithm
,	O
,	O
where	O
P	O
is	O
a	O
permutation	B-Algorithm
matrix	I-Algorithm
,	O
is	O
a	O
(	O
permuted	O
)	O
arrowhead	B-Algorithm
matrix	I-Algorithm
.	O
</s>
<s>
A	O
symmetric	O
arrowhead	B-Algorithm
matrix	I-Algorithm
is	O
irreducible	O
if	O
for	O
all	O
i	O
and	O
for	O
all	O
.	O
</s>
<s>
The	O
Julia	B-Application
version	O
of	O
the	O
software	O
is	O
available	O
.	O
</s>
<s>
Let	O
A	O
be	O
an	O
irreducible	O
real	O
symmetric	O
arrowhead	B-Algorithm
matrix	I-Algorithm
.	O
</s>
<s>
If	O
for	O
some	O
i	O
,	O
the	O
inverse	O
is	O
a	O
permuted	O
irreducible	O
real	O
symmetric	O
arrowhead	B-Algorithm
matrix	I-Algorithm
:	O
</s>
