orthogonal group

《Class Field Theory》 · 印刷第 7—8 页 Section 1.2.2「Unitary and Orthogonal Groups」，正交矩阵与正交群定义；本段为实数域上正定标准内积的情形

In a similar fashion, an $n\times n$ real matrix $A$ is said to be orthogonal if the column vectors of $A$ are orthonormal. […] The collection of all orthogonal matrices forms a closed subgroup of $GL(n;\mathbb C)$, which we call the orthogonal group and denote by $O(n)$.