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Orthogonal group
In
mathematics
, the
orthogonal group
in dimension , denoted , is the
group
of
distance-preserving transformations
of a
Euclidean space
of dimension that preserve a fixed point, where the group operation is given by
composing
transformations. Equivalently, it is the group of
orthogonal matrices
, where the group operation is given by
matrix multiplication
, and an orthogonal matrix is a
real
matrix whose
inverse
equals its
transpose
.
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