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India LIMIT
2019 LIMIT
2019 LIMIT Category C
Problem 7
4x4 orthogonal matrices over Z
4x4 orthogonal matrices over Z
Source: LIMIT 2019 CCS2 P7
April 28, 2021
Matrices
linear algebra
Problem Statement
Let
O
(
4
,
Z
)
O(4,\mathbb Z)
O
(
4
,
Z
)
be the set of all
4
×
4
4\times4
4
×
4
orthogonal matrices over
Z
\mathbb Z
Z
, i.e.,
A
t
A
=
I
=
A
A
t
A^tA=I=AA^t
A
t
A
=
I
=
A
A
t
. Then
∣
O
(
4
,
Z
)
∣
|O(4,\mathbb Z)|
∣
O
(
4
,
Z
)
∣
is
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