This article is about a particular group, i.e., a group unique upto isomorphism. View specific information (such as linear representation theory, subgroup structure) about this group
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This group is defined as the group of matrices with real entries such that is the identity matrix. Equivalently, it can be defined as:
In fact, there are only two possible forms of such matrices:
The subgroup of matrices with determinant (i.e., the matrices with ) is the special orthogonal group . It has index two and is isomorphic to the circle group.
This group can be defined in the following other ways: