Update cheatsheet.fr.md

12.temporary_ins/04-math-tools/70.systems-of-differential-equations/40.parallel-1/cheatsheet.fr.md

@@ -75,24 +75,24 @@ $`M^0 = I_m`$ matrice identité de dimension $`m\times m`$.
 $`\begin{align} \quad\;\; & =\;\dfrac{1}{0!}\;\begin{pmatrix} 1 & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 & 1 \\ \end{pmatrix} + 
 \dfrac{1}{1!}\;\begin{pmatrix}  \lambda_1 & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 & \lambda_m \\ \end{pmatrix} + \cdots \\
 & \\
-& \quad\;\; \cdots +\dfrac{1}{2!}\;\begin{pmatrix} \lambda_1 & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 & \lambda_m \\ \end{pmatrix}^2
+& \quad\quad\; \cdots +\dfrac{1}{2!}\;\begin{pmatrix} \lambda_1 & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 & \lambda_m \\ \end{pmatrix}^2
 +\cdots \\
 & \\
-& \quad\;\; \cdots + \dfrac{1}{k!}\;\begin{pmatrix} \lambda_1 & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 & \lambda_m \\ \end{pmatrix}^k + \cdots
+& \quad\quad\; \cdots + \dfrac{1}{k!}\;\begin{pmatrix} \lambda_1 & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 & \lambda_m \\ \end{pmatrix}^k + \cdots
 \end{align}`$    
 <br>
 <br>
 $`\begin{align} \quad\;\; & = \;\dfrac{1}{0!}\;\begin{pmatrix} 1 & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 & 1 \\ \end{pmatrix} + 
 \dfrac{1}{1!}\;\begin{pmatrix}  \lambda_1 & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 & \lambda_m \\ \end{pmatrix} + \cdots \\
 & \\
-& \quad\;\; \cdots +\dfrac{1}{2!}\;\begin{pmatrix} \lambda_1^2 & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 & \lambda_m^2 \\ \end{pmatrix}
+& \quad\quad\; \cdots +\dfrac{1}{2!}\;\begin{pmatrix} \lambda_1^2 & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 & \lambda_m^2 \\ \end{pmatrix}
 +\cdots \\
 & \\
-& \quad\;\; \cdots + \dfrac{1}{k!}\;\begin{pmatrix} \lambda_1^k & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 & \lambda_m^k \\ \end{pmatrix} + \cdots
+& \quad\quad\; \cdots + \dfrac{1}{k!}\;\begin{pmatrix} \lambda_1^k & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 & \lambda_m^k \\ \end{pmatrix} + \cdots
 \end{align}`$    
 <br>
 <br>
-$`\quad\;\; & = \;\begin{pmatrix} \dfrac{1}{n!}\sum_{n=0}^{+\infty}\lambda_1^n & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 & \dfrac{1}{n!}\sum_{n=0}^{+\infty}\lambda_m^n \\ \end{pmatrix}`$
+$`\quad\;\; = \;\begin{pmatrix} \dfrac{1}{n!}\sum_{n=0}^{+\infty}\,\lambda_1^n & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 & \dfrac{1}{n!}\sum_{n=0}^{+\infty}\,\lambda_m^n \\ \end{pmatrix}`$