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An explicit decomposition formula of a matrix in
G
L
2
(
Z
)
GL_{2}\left(\mathbb{Z}\right)
G
L
2
β
(
Z
)
Authors
Dominique Fosse
Publication date
10 April 2023
Publisher
View
on
arXiv
Abstract
Given
A
:
=
(
1
1
0
1
)
A:=\left(\begin{smallmatrix}1&1\\0&1\end{smallmatrix}\right)
A
:=
(
1
0
β
1
1
β
)
,
B
:
=
(
1
0
1
1
)
B:=\left(\begin{smallmatrix}1&0\\1&1\end{smallmatrix}\right)
B
:=
(
1
1
β
0
1
β
)
and
C
:
=
(
1
0
0
β
1
)
C:=\left(\begin{smallmatrix}1&0\\0&-1\end{smallmatrix}\right)
C
:=
(
1
0
β
0
β
1
β
)
three elements of
G
L
2
(
Z
)
GL_{2}\left(\mathbb{Z}\right)
G
L
2
β
(
Z
)
, we propose an explicit formula that provides the decomposition of any
M
β
G
L
2
(
Z
)
M\in GL_{2}\left(\mathbb{Z}\right)
M
β
G
L
2
β
(
Z
)
in
β¨
A
,
B
,
C
β©
\langle A,B,C\rangle
β¨
A
,
B
,
C
β©
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oai:arXiv.org:2304.04804
Last time updated on 14/04/2023