General linear group

Japanese: 一般線形群 - いっぱんせんけいぐん
General linear group

…All n -th order square matrices with real entries that have an inverse form a group under matrix multiplication. This is called the general linear group over the real numbers. All n -th order square matrices with real entries whose determinant is 1 form a subgroup of the general linear group. …

From [Linear group]

GL ( n , C ) is equal to { A | A is an n -th order square matrix on C that has an inverse}, so it becomes a group by matrix multiplication. This is called the n -th order general linear group on C. A subgroup of GL ( n , C ) is called a linear group. …

*Some of the terminology that mentions "general linear groups" is listed below.

Source | Heibonsha World Encyclopedia 2nd Edition | Information

Japanese:

…実数を成分とするn次の正方行列で逆行列をもつものの全体は行列の積に関して群を作る。これを実数体上の一般線形群という。実数を成分とするn次正方行列で,その行列式の値が1であるものの全体は一般線形群の部分群を作る。…

【線形群】より

GL(nC)は{AAC上のn次正方行列で,逆行列をもつもの}と一致するから,行列の乗法によって群になる。これをC上のn次一般線形群という。GL(nC)の部分群を線形群と呼ぶ。…

※「一般線形群」について言及している用語解説の一部を掲載しています。

出典|株式会社平凡社世界大百科事典 第2版について | 情報

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