英和和英

名詞

orthogonal group (複数形 orthogonal groups)

1. (group theory) For 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.
   • 1998, Robert L. Griess, Jr., Twelve Sporadic Groups, Springer, page 4,

     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.

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

     Theorem 7.4. Let n ≥ 1. For odd primes ${\displaystyle p\not \equiv \pm 1{\pmod {24}}}$ the odd-dimensional orthogonal groups ${\displaystyle O_{2n+1}(p)}$ possess GA-realizations over ${\displaystyle \mathbb {Q} }$.

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

     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.