Last Updated：2025/12/03

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(group theory) For given field F and order n, the group of invertible n×n matrices, with the group operation of matrix multiplication.

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general linear group

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Source Word

general linear group

Noun

Japanese Meaning

与えられた体 F 上の n 次正方行列のうち、逆行列を持つ行列全体で、行列の積を群演算とする群。

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Google Translation / DeepL Translation

群論において、一般線形群 GL_n(F) は体F上の可逆なn×n行列全体であり、群演算は行列の積です。

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Sense（1）

Often Lie groups arise as subgroups of certain larger Lie groups; for example, the orthogonal groups are subgroups of the general linear groups of all invertible matrices.

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general linear groups

（ plural ）

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general linear group

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