vault backup: 2026-01-23 20:15:41

编写小组/讲义/正交及二次型（解析版）.md

@@ -70,7 +70,7 @@ $$\begin{align*}
 $$\boldsymbol{\varepsilon}_k = \frac{\boldsymbol{u}_k}{\|\boldsymbol{u}_k\|},\quad 
 k=1,2,3,\dots,p$$
 还有另一个更加常用的正交化法：$$\begin{aligned}
-\boldsymbol u_1&=\boldsymbol\alpha_1,\boldsymbol\varepsilon_1=\dfrac{\boldsymbol u_1}{\|\boldsymbol u_1\|},\\
+\boldsymbol u_1&=\langle\boldsymbol\alpha_1,\boldsymbol\varepsilon_1\rangle=\dfrac{\boldsymbol u_1}{\|\boldsymbol u_1\|},\\
 \boldsymbol u_k&=\boldsymbol\alpha_k-\sum_{i=1}^{k-1}\langle\boldsymbol\varepsilon_i,\boldsymbol\alpha_k\rangle\boldsymbol\varepsilon_i,\boldsymbol\varepsilon_k=\dfrac{\boldsymbol u_k}{\|\boldsymbol u_k\|}(k=2,3,\cdots,p).
 \end{aligned}$$
 ### **例子**