Naive Lie Theory
《Naive Lie Theory》 · 印刷第 1 页 1.1.1 的基域约定及第 23 页 Section 2.1 的例 (3)、(4)(h)；原书 ${}^tX$ 表示转置，$1_n$ 表示单位矩阵
Let $k$ be an algebraically closed field and put $V=k^n$. […] View the set $\mathbf M_n$ of all $n\times n$-matrices as $k^{n^2}$ in the obvious manner. For $X\in\mathbf M_n$ let $D(X)$ be its determinant. Then $D$ is a regular function on $\mathbf M_n$. The general linear group $\mathbf{GL}_n$ is the principal open set $\{X\in\mathbf M_n\mid D(X)\ne0\}$, with matrix multiplication as group operation. […] (h) the symplectic group $\mathbf{Sp}_{2n}=\{X\in\mathbf{GL}_{2n}\mid {}^tXJX=J\}$, where $J$ is the matrix $\begin{pmatrix}0&1_n\\-1_n&0\end{pmatrix}$.