From b4772c2457b5f7797622f455f285b11f8765d28d Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E7=8E=8B=E8=BD=B2=E6=A5=A0?= Date: Wed, 21 Jan 2026 00:46:21 +0800 Subject: [PATCH] vault backup: 2026-01-21 00:46:21 --- 编写小组/讲义/矩阵相似变换（解析版）.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/编写小组/讲义/矩阵相似变换（解析版）.md b/编写小组/讲义/矩阵相似变换（解析版）.md index 9994c0b..101c79b 100644 --- a/编写小组/讲义/矩阵相似变换（解析版）.md +++ b/编写小组/讲义/矩阵相似变换（解析版）.md @@ -198,7 +198,7 @@ $$ 由 $\left[\boldsymbol{\beta}_1\;\boldsymbol{\beta}_2\;\dots\;\boldsymbol{\beta}_n\right]=\left[\boldsymbol{\alpha}_1\;\boldsymbol{\alpha}_2\;\dots\;\boldsymbol{\alpha}_n\right]C$，且 $$ \left[T(\boldsymbol{\alpha}_1)\;T(\boldsymbol{\alpha}_2)\;\dots\;T(\boldsymbol{\alpha}_n)\right]=\left[\boldsymbol{\alpha}_1\;\boldsymbol{\alpha}_2\;\dots\;\boldsymbol{\alpha}_n\right]A,$$ $$ \left[T(\boldsymbol{\beta}_1)\;T(\boldsymbol{\beta}_2)\;\dots\;T(\boldsymbol{\beta}_n)\right]=\left[\boldsymbol{\beta}_1\;\boldsymbol{\beta}_2\;\dots\;\boldsymbol{\beta}_n\right]B.$$ -由 $\boldsymbol \beta_i=c_{1i}\boldsymbol\alpha_1+\cdots+c_{ni}\boldsymbol\alpha_n$ 及线性变换的定义可知$$T(\boldsymbol\beta_i)=c_{1i}T(\boldsymbol\alpha_1)+\cdots+c_{ni}T(\boldsymbol\alpha_n),$$ +由 $\boldsymbol \beta_i=c_{1i}\boldsymbol\alpha_1+\cdots+c_{ni}\boldsymbol\alpha_n$ 及线性变换的定义可知$$T(\boldsymbol\beta_i)=c_{1i}T(\boldsymbol\alpha_1)+\cdots+c_{ni}T(\boldsymbol\alpha_n)=[T(\boldsymbol\alpha_1)\ \cdots T(\boldsymbol\alpha_n)]\begin{bmatrix}c_{1i}\\\vdots\\c_{ni}\end{bmatrix},$$ 从而：$$ \begin{aligned} \left[T(\boldsymbol{\beta}_1)\;T(\boldsymbol{\beta}_2)\;\dots\;T(\boldsymbol{\beta}_n)\right]&=\left[T(\boldsymbol{\alpha}_1)\;T(\boldsymbol{\alpha}_2)\;\dots\;T(\boldsymbol{\alpha}_n)\right]C \\