Oct 6, 2013
In mathematics, the orthogonal group is the group of distance-preserving transformations of Euclidean space which preserve the origin, where the group operation is given by composing transformations. Equivalently, it is the group of orthogonal matrices of a given dimension, where the group operation is given by matrix multiplication. An orthogonal matrix is a real matrix whose inverse equals its transpose. The term "orthogonal group" may also refer to a generalization of the above case: the group of invertible linear operators which preserve a non-degenerate symmetric bilinear form or quadratic form[1] on a vector space over a field.