<s>
In	O
mathematics	O
,	O
a	O
signature	B-Algorithm
matrix	I-Algorithm
is	O
a	O
diagonal	B-Algorithm
matrix	I-Algorithm
whose	O
diagonal	O
elements	O
are	O
plus	O
or	O
minus	O
1	O
,	O
that	O
is	O
,	O
any	O
matrix	O
of	O
the	O
form	O
:	O
</s>
<s>
Any	O
such	O
matrix	O
is	O
its	O
own	O
inverse	O
,	O
hence	O
is	O
an	O
involutory	B-Algorithm
matrix	I-Algorithm
.	O
</s>
<s>
It	O
is	O
consequently	O
a	O
square	O
root	O
of	O
the	O
identity	B-Algorithm
matrix	I-Algorithm
.	O
</s>
<s>
Noting	O
that	O
signature	O
matrices	O
are	O
both	O
symmetric	B-Algorithm
and	O
involutory	O
,	O
they	O
are	O
thus	O
orthogonal	B-Algorithm
.	O
</s>
<s>
Consequently	O
,	O
any	O
linear	O
transformation	O
corresponding	O
to	O
a	O
signature	B-Algorithm
matrix	I-Algorithm
constitutes	O
an	O
isometry	O
.	O
</s>
<s>
Geometrically	O
,	O
signature	O
matrices	O
represent	O
a	O
reflection	B-Algorithm
in	O
each	O
of	O
the	O
axes	O
corresponding	O
to	O
the	O
negated	O
rows	O
or	O
columns	O
.	O
</s>
