orthogonal group

plural orthogonal groups

1. group theoryFor given n and field F (especially where F is the real numbers), the group of n × n orthogonal matrices with elements in F, where the group operation is matrix multiplication.

   The normalizer of the full orthogonal group within the general linear group can be shown to consist of all (commutative) products of spherical dilatations and orthogonal transformations.

   2007, Marcelo Epstein, Marek Elzanowski, Material Inhomogeneities and their Evolution: A Geometric Approach, Springer, page 106

   2 more examples

   The symbol O^ε(n,q) for orthogonal groups has been well established in finite group theory as and, throughout the mathematics community, O(n, K) stands for an orthogonal group when K is the real or complex field.

   1998, Robert L. Griess, Jr., Twelve Sporadic Groups, Springer, page 4

   Theorem 7.4. Let n ≥ 1. For odd primes p#92;not#92;equiv#92;pm 1#92;pmod#123;24#125; the odd-dimensional orthogonal groups O#95;#123;2n#43;1#125;(p) possess GA-realizations over #92;mathbb#123;Q#125;.

   1999, Gunter Malle, B.H. Matzat, Inverse Galois Theory, Springer, page 146