Commit 8d63183c authored by Claude Meny's avatar Claude Meny

Update cheatsheet.fr.md

parent 19289172
Pipeline #16420 canceled with stage
......@@ -68,7 +68,7 @@ $`M^0 = I_m`$ matrice identité de dimension $`m\times m`$.
##### $`M`$ est diagonale :
*$`\mathbf{M = \begin{pmatrix} \lambda_1 & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 & \lambda_m \\ \end{pmatrix}}`$*
*$`\large{\mathbf{M = \begin{pmatrix} \lambda_1 & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 & \lambda_m \\ \end{pmatrix}}}`$*
**$`\large{\mathbf{e^{\,M}}}`$** $`\displaystyle\; = \sum_{n=0}^{+\infty}\dfrac{M^n}{n!}`$
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......@@ -95,11 +95,19 @@ $`\begin{align} \quad\;\; & = \;\dfrac{1}{0!}\;\begin{pmatrix} 1 & 0 & 0 \\ 0 &
$`\quad\;\; = \;\begin{pmatrix} \displaystyle\sum_{n=0}^{+\infty}\,\dfrac{\lambda_1^n}{n!} & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 & \displaystyle\sum_{n=0}^{+\infty}\,\dfrac{\lambda_m^n}{n!} \\ \end{pmatrix}`$
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**$`\large{\mathbf{e^{\,M} = \;\begin{pmatrix} e^{\,\lambda_1} & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 & e^{\lambda_m} \\ \end{pmatrix}}}`$**
**$`\large{\mathbf{e^{\,M} = \;\begin{pmatrix} e^{\,\lambda_1} & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 & e^{\,\lambda_m} \\ \end{pmatrix}}}`$**
##### $`M`$ est non diagonale, mais diagonalisable :
*$`\large{\exists P\,}`$* **$`\large{\; M = P\;\begin{pmatrix} \lambda_1 & 0 & 0 \\ 0 & \cdots & 0 \\ 0 & 0 & \lambda_m \\ \end{pmatrix} \;P^{-1}}}`$**
avec les lmbdas valeurs propres et P ... à terminer, en fonction de ce qu'on met avant.
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