<s>
In	O
mathematics	O
,	O
especially	O
linear	B-Language
algebra	I-Language
,	O
the	O
exchange	O
matrices	O
(	O
also	O
called	O
the	O
reversal	B-Algorithm
matrix	I-Algorithm
,	O
backward	O
identity	O
,	O
or	O
standard	O
involutory	O
permutation	O
)	O
are	O
special	O
cases	O
of	O
permutation	B-Algorithm
matrices	I-Algorithm
,	O
where	O
the	O
1	O
elements	O
reside	O
on	O
the	O
antidiagonal	O
and	O
all	O
other	O
elements	O
are	O
zero	O
.	O
</s>
<s>
In	O
other	O
words	O
,	O
they	O
are	O
'	O
row-reversed	O
'	O
or	O
'	O
column-reversed	O
'	O
versions	O
of	O
the	O
identity	B-Algorithm
matrix	I-Algorithm
.	O
</s>
<s>
Exchange	O
matrices	O
are	O
symmetric	B-Algorithm
;	O
that	O
is	O
,	O
JnT	O
=	O
Jn	O
.	O
</s>
<s>
In	O
particular	O
,	O
Jn	O
is	O
an	O
involutory	B-Algorithm
matrix	I-Algorithm
;	O
that	O
is	O
,	O
Jn−1	O
=	O
Jn	O
.	O
</s>
<s>
An	O
exchange	B-Algorithm
matrix	I-Algorithm
is	O
the	O
simplest	O
anti-diagonal	B-Algorithm
matrix	I-Algorithm
.	O
</s>
<s>
Any	O
matrix	O
A	O
satisfying	O
the	O
condition	O
AJ	O
=	O
JA	O
is	O
said	O
to	O
be	O
centrosymmetric	B-Algorithm
.	O
</s>
<s>
Any	O
matrix	O
A	O
satisfying	O
the	O
condition	O
AJ	O
=	O
JAT	O
is	O
said	O
to	O
be	O
persymmetric	B-Algorithm
.	O
</s>
<s>
Symmetric	B-Algorithm
matrices	I-Algorithm
A	O
that	O
satisfy	O
the	O
condition	O
AJ	O
=	O
JA	O
are	O
called	O
bisymmetric	B-Algorithm
matrices	O
.	O
</s>
<s>
Bisymmetric	B-Algorithm
matrices	O
are	O
both	O
centrosymmetric	B-Algorithm
and	O
persymmetric	B-Algorithm
.	O
</s>
