general linear group

《代数学引论》 · 第 24 页 · 例 5

元素在数域 $P$ 中全体 $n$ 级可逆矩阵对于矩阵的乘法成一个群，这个群记为 $GL_n(P)$，称为 $n$ 级一般线性群；

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《Abstract Algebra》 · 第 34–35 页 · Section 1.4「Matrix Groups」

All the vector space theory, the theory of matrices and linear transformations and the theory of determinants when the scalars come from $\mathbb R$ is true, mutatis mutandis, when the scalars come from an arbitrary field $F$. […] For each $n\in\mathbb Z^+$ let $GL_n(F)$ be the set of all $n\times n$ matrices whose entries come from $F$ and whose determinant is nonzero, i.e., $GL_n(F)=\{A\mid A\text{ is an }n\times n\text{ matrix with entries from }F\text{ and }\det(A)\ne0\}$, where the determinant of any matrix $A$ with entries from $F$ can be computed by the same formulas used when $F=\mathbb R$. […] Thus $GL_n(F)$ is a group under matrix multiplication, called the general linear group of degree $n$.