From 450599ad51bc0f0592e1a54ddbdd070dc08eac40 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E5=88=98=E6=9F=AF=E5=A6=A4?= <2503393720@qq.com>
Date: Sat, 17 Jan 2026 14:34:04 +0800
Subject: [PATCH] vault backup: 2026-01-17 14:34:04

---
 素材/正交矩阵和施密特正交化法.md | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/素材/正交矩阵和施密特正交化法.md b/素材/正交矩阵和施密特正交化法.md
index 1b77157..92205cb 100644
--- a/素材/正交矩阵和施密特正交化法.md
+++ b/素材/正交矩阵和施密特正交化法.md
@@ -70,11 +70,11 @@ $$
 设 A为 n阶正交矩阵（n≥2），则
 $$\boldsymbol{A}^\top\boldsymbol{A}=\boldsymbol{E}$$
 又由伴随矩阵与逆矩阵的关系：
-$$A^{-1} = \frac{1}{|A|} \text{adj}(A)$$ 
+$$\boldsymbol A^{-1} = \frac{1}{|A|}\boldsymbol{A}^*$$ 
 联立得
-$$\boldsymbol{A}\top\boldsymbol= \frac{1}{|A|} \text{adj}(A)$$
+$$\boldsymbol{A}^T= \frac{1}{|A|}\boldsymbol A^*$$
 正交矩阵的行列式满足 $\frac{1}{|A|} =±1$，故
-$adj(A)=(detA)AT=±AT$
+$A^*={|A|}A^T=±A^T$ 
 由伴随矩阵的定义，其第 (j,i)元为 aij​的代数余子式 Aij​，而 ±AT的第 (j,i)元为 ±aij​。比较对应元素得
 $$Aij​=±aij​,i,j=1,2,…,n.$$
 证毕