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

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

@@ -68,9 +68,25 @@ $`M^0 = I_m`$ matrice identité de dimension $`m\times m`$.
 
 $`M`$ est diagonale :
 
-$`M=\begin{pmatrix} \lambda_1 & cdots & 0 \\ \vdots & \ddots & \vdots \\ 0 & & cdots & 0 \\ \end{pmatrix}`$
-
-$`e^{\,M}`$
+$`M=\begin{pmatrix} \lambda_1 & \cdots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \cdots & \lambda_m \\ \end{pmatrix}`$
+
+ou  
+
+$`M=\begin{pmatrix} \lambda_1 & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & \cdots & \lambda_m \\ \end{pmatrix}`$
+
+$`e^{\,M}=
+\begin{pmatrix}  & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & \cdots & 1 \\ \end{pmatrix}
++ 
+\begin{pmatrix}  & \lambda_1 & 0 \\ 0 & \ddots & 0 \\ 0 & \cdots & \lambda_m \\ \end{pmatrix}
++
+\dfrac{1}{2!}\begin{pmatrix}  & \lambda_1 & 0 \\ 0 & \ddots & 0 \\ 0 & \cdots & \lambda_m \\ \end{pmatrix}^2
++
+\cdots
++
+\dfrac{1}{k!}\begin{pmatrix}  & \lambda_1 & 0 \\ 0 & \ddots & 0 \\ 0 & \cdots & \lambda_m \\ \end{pmatrix}^k
++
+\cdots
+`$