orthogonal group

英語（米国） (en-US) 英語（イギリス） (en-GB)

名詞

(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.

日本語の意味

nと体F（特に実数の場合）に対して、Fの元を要素とするn×n直交行列全体からなる群。群の演算は行列の積で定義される。

英語の意味

(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.

このボタンはなに？

The orthogonal group O(n) consists of all n × n matrices with real entries that preserve the Euclidean inner product under matrix multiplication.

直交行列群 O(n) は、行列の積においてユークリッド内積を保つ実数成分の n × n 行列全体からなる。

詳細

意味（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.

The symbol Oε(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.

詳細

orthogonal groups （ plural ）