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docs: 修改行列式图示
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yhwu-is committed Oct 19, 2024
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3 changes: 2 additions & 1 deletion 讲义/专题/10 行列式.tex
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Expand Up @@ -30,9 +30,10 @@ \section{导言}
$$
显然是将每个坐标轴拉长到了原来的 $\lambda_i$ 倍,体积变化的倍数便是 $\lambda_1 \lambda_2 \cdots \lambda_n$. 从直观上,线性变换使得每块区域的体积(实际上是 $n$ 维的体积)都会以相同的倍数变化,所以这样的一个与矩阵相关的量理应是存在的. 而且显然地应该满足矩阵复合的体积变化倍数等于体积变化倍数的乘积,即 $\det(AB) = \det A \cdot \det B$,而我们之后严格定义行列式后也会证明这一点.

最方便的做法便是取定单位正方形,考虑变换后的几个向量形成的平行四边形面积(或者高维空间的对应物)
最方便的做法便是取定单位正方形,考虑变换后的几个向量形成的平行四边形面积(或者高维空间的对应物)

\begin{figure}[htbp]
\centering
\begin{tikzpicture}[>=Stealth, scale=1]
\draw[->] (-0.5, 0) -- (1.5, 0);
\draw[->] (0, -0.5) -- (0, 1.5);
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