<s>
In	O
mathematics	O
,	O
especially	O
in	O
linear	B-Language
algebra	I-Language
and	O
matrix	B-Architecture
theory	I-Architecture
,	O
the	O
duplication	B-Algorithm
matrix	I-Algorithm
and	O
the	O
elimination	B-Algorithm
matrix	I-Algorithm
are	O
linear	B-Architecture
transformations	I-Architecture
used	O
for	O
transforming	O
half-vectorizations	O
of	O
matrices	B-Architecture
into	O
vectorizations	B-Algorithm
or	O
(	O
respectively	O
)	O
vice	O
versa	O
.	O
</s>
<s>
The	O
duplication	B-Algorithm
matrix	I-Algorithm
is	O
the	O
unique	O
matrix	O
which	O
,	O
for	O
any	O
symmetric	B-Algorithm
matrix	I-Algorithm
,	O
transforms	O
into	O
:	O
</s>
<s>
The	O
explicit	O
formula	O
for	O
calculating	O
the	O
duplication	B-Algorithm
matrix	I-Algorithm
for	O
a	O
matrix	O
is	O
:	O
</s>
<s>
Here	O
is	O
a	O
C++	B-Language
function	O
using	O
Armadillo	B-Language
(	O
C++	B-Language
library	O
)	O
:	O
</s>
<s>
An	O
elimination	B-Algorithm
matrix	I-Algorithm
is	O
a	O
matrix	O
which	O
,	O
for	O
any	O
matrix	O
,	O
transforms	O
into	O
:	O
</s>
<s>
Here	O
is	O
a	O
C++	B-Language
function	O
using	O
Armadillo	B-Language
(	O
C++	B-Language
library	O
)	O
:	O
</s>
