<s>
In	O
linear	B-Language
algebra	I-Language
,	O
similarity	B-Algorithm
invariance	I-Algorithm
is	O
a	O
property	O
exhibited	O
by	O
a	O
function	O
whose	O
value	O
is	O
unchanged	O
under	O
similarities	O
of	O
its	O
domain	O
.	O
</s>
<s>
That	O
is	O
,	O
is	O
invariant	O
under	O
similarities	O
if	O
where	O
is	O
a	O
matrix	B-Architecture
similar	B-Algorithm
to	O
A	O
.	O
</s>
<s>
A	O
more	O
colloquial	O
phrase	O
that	O
means	O
the	O
same	O
thing	O
as	O
similarity	B-Algorithm
invariance	I-Algorithm
is	O
"	O
basis	O
independence	O
"	O
,	O
since	O
a	O
matrix	B-Architecture
can	O
be	O
regarded	O
as	O
a	O
linear	B-Architecture
operator	I-Architecture
,	O
written	O
in	O
a	O
certain	O
basis	O
,	O
and	O
the	O
same	O
operator	O
in	O
a	O
new	O
basis	O
is	O
related	O
to	O
one	O
in	O
the	O
old	O
basis	O
by	O
the	O
conjugation	O
,	O
where	O
is	O
the	O
transformation	B-Algorithm
matrix	I-Algorithm
to	O
the	O
new	O
basis	O
.	O
</s>
