<s>
So	O
for	O
real	B-Architecture
matrices	I-Architecture
similar	O
by	O
some	O
real	O
matrix	O
,	O
consimilarity	B-Algorithm
is	O
the	O
same	O
as	O
matrix	B-Algorithm
similarity	I-Algorithm
.	O
</s>
<s>
Like	O
ordinary	O
similarity	O
,	O
consimilarity	B-Algorithm
is	O
an	O
equivalence	O
relation	O
on	O
the	O
set	O
of	O
matrices	B-Architecture
,	O
and	O
it	O
is	O
reasonable	O
to	O
ask	O
what	O
properties	O
it	O
preserves	O
.	O
</s>
<s>
The	O
theory	O
of	O
ordinary	O
similarity	O
arises	O
as	O
a	O
result	O
of	O
studying	O
linear	B-Architecture
transformations	I-Architecture
referred	O
to	O
different	O
bases	O
.	O
</s>
<s>
Consimilarity	B-Algorithm
arises	O
as	O
a	O
result	O
of	O
studying	O
antilinear	O
transformations	O
referred	O
to	O
different	O
bases	O
.	O
</s>
<s>
A	O
matrix	O
is	O
consimilar	O
to	O
itself	O
,	O
its	O
complex	O
conjugate	O
,	O
its	O
transpose	O
and	O
its	O
adjoint	B-Algorithm
matrix	I-Algorithm
.	O
</s>
<s>
Every	O
matrix	O
is	O
consimilar	O
to	O
a	O
real	O
matrix	O
and	O
to	O
a	O
Hermitian	B-Algorithm
matrix	I-Algorithm
.	O
</s>
<s>
There	O
is	O
a	O
standard	O
form	O
for	O
the	O
consimilarity	B-Algorithm
class	O
,	O
analogous	O
to	O
the	O
Jordan	O
normal	O
form	O
.	O
</s>
