换行

5/index.md

@@ -10,26 +10,32 @@ $$\begin{aligned}&U=A^{(n)}=L_{n-1}\cdots L_{2}L_{1}A\\&L=L_{1}^{-1}L_{2}^{-1}\c
 
 则有 $A{=}LDM{=}LDL^\mathrm{T}$
 
-$$\begin{aligned}D=&\begin{pmatrix}\sqrt{u_{11}}&&&&\\&\sqrt{u_{22}}&&&\\&&\ddots&&\\&&&\sqrt{u_{m}}\end{pmatrix}\begin{pmatrix}\sqrt{u_{11}}&&&\\&\sqrt{u_{22}}&&\\&&\ddots&\\&&&\sqrt{u_{nm}}\end{pmatrix}\\&=D^{\frac12}D^{\frac12}\end{aligned}$$
+$$
+\begin{aligned}D=&\begin{pmatrix}\sqrt{u_{11}}&&&&\\&\sqrt{u_{22}}&&&\\&&\ddots&&\\&&&\sqrt{u_{m}}\end{pmatrix}\begin{pmatrix}\sqrt{u_{11}}&&&\\&\sqrt{u_{22}}&&\\&&\ddots&\\&&&\sqrt{u_{nm}}\end{pmatrix}\\&=D^{\frac12}D^{\frac12}\end{aligned}
+$$
 
-Cholesky分解：$A=LD^\frac12D^\frac12L^\mathrm{T}=(LD^\frac12)(LD^\frac12)^\mathrm{T}=GG^\mathrm{T}$
+Cholesky分解： $A=LD^\frac12D^\frac12L^\mathrm{T}=(LD^\frac12)(LD^\frac12)^\mathrm{T}=GG^\mathrm{T}$
 
 
 #### 向量范数
 
-$$\begin{aligned}
+$$
+\begin{aligned}
 &\left\|x\right\|_{\infty}=\max_{1\leq i\leq n}\left|x_{i}\right| \\
 &\left\|x\right\|_1=\sum_{i=1}^n\left|x_i\right| \\
 &\left\|x\right\|_2=(\sum_{i=1}^nx_i^2)^{\frac12} 
-\end{aligned}$$
+\end{aligned}
+$$
 
 #### 矩阵范数
 
-$$\begin{aligned}
+$$
+\begin{aligned}
 &\left\|A\right\|_{\infty}=\max_{1\leq i\leq n}\sum_{j=1}^{n}\left|a_{ij}\right| \\
 &\left\|A\right\|_1=\max_{1\leq j\leq n}\sum_{i=1}^n\left|a_{ij}\right| \\
 &\left\|A\right\|_{2}=\sqrt{\lambda_{\max}\left(A^{\mathrm{T}}A\right)} \\
 &\left\|A\right\|_{\mathrm{F}}=\sqrt{\sum_{i,j=1}^{n}a_{ij}^{2}}
-\end{aligned}$$
+\end{aligned}
+$$
 
 **谱半径**  $\rho(A)=\max_{1\leq i\leq n}\left|\lambda_i\right|$