| 31. | Moreover, since composition of rotations corresponds to matrix multiplication, the rotation group is isomorphic to the special orthogonal group.
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| 32. | Every such group is a subgroup of the orthogonal group O ( 2 ), including O ( 2 ) itself.
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| 33. | One is rotation group, or more generally of double cover of the generalized special orthogonal group on spaces with metric signature.
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| 34. | The set of orthogonal matrices forms a group O ( " n " ), known as the orthogonal group.
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| 35. | The term "'rotation group "'can be used to describe either the special or general orthogonal group.
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| 36. | The set of all orthogonal matrices of size with determinant + 1 or-1 forms the ( general ) orthogonal group.
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| 37. | The properties of the spin representations depend, in a subtle way, on the dimension and signature of the orthogonal group.
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| 38. | An archetypical irreducible reductive dual pair of type I consists of an orthogonal group and a symplectic group and is constructed analogously.
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| 39. | The "'indefinite special orthogonal group "', is the subgroup of consisting of all elements with determinant 1.
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| 40. | Any subgroup containing at least one non-zero translation must be infinite, but subgroups of the orthogonal group can be finite.
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