Let be a non-degenerate symmetric bilinear form over the real vector space . A linear transformation is said to preserve if for all vectors . The subgroup of the general linear group consisting of all linear transformations that preserve is called the orthogonal group with respect to , and denoted .
If is also positive definite (i.e., is an inner product), then is equivalent to the group of invertible linear transformations that preserve the standard inner product on , and in this case the group is usually denoted .
|Date of creation||2013-03-22 12:25:54|
|Last modified on||2013-03-22 12:25:54|
|Last modified by||djao (24)|