Commit 78e0e4d8 authored by Claude Meny's avatar Claude Meny

Update cheatsheet.fr.md

parent 1cce2394
Pipeline #16407 canceled with stage
...@@ -70,7 +70,9 @@ $`M`$ est diagonale : ...@@ -70,7 +70,9 @@ $`M`$ est diagonale :
$`M = \begin{pmatrix} \lambda_1 & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 & \lambda_m \\ \end{pmatrix}`$ $`M = \begin{pmatrix} \lambda_1 & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 & \lambda_m \\ \end{pmatrix}`$
$`\begin{align} e^{\,M} & = \sum_{n=0}^{+\infty}\dfrac{M^n}{n!} \\ $`e^{\,M} & = \sum_{n=0}^{+\infty}\dfrac{M^n}{n!}`$
<br>
$`\begin{align} \quad\quad & = \sum_{n=0}^{+\infty}\dfrac{M^n}{n!} \\
& \\ & \\
& = \begin{pmatrix} 1 & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 & 1 \\ \end{pmatrix} + & = \begin{pmatrix} 1 & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 & 1 \\ \end{pmatrix} +
\begin{pmatrix} \lambda_1 & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 & \lambda_m \\ \end{pmatrix} + \cdots \\ \begin{pmatrix} \lambda_1 & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 & \lambda_m \\ \end{pmatrix} + \cdots \\
...@@ -86,10 +88,10 @@ $`\begin{align}\quad\quad\quad & = \sum_{n=0}^{+\infty}\dfrac{M^n}{n!} \\ ...@@ -86,10 +88,10 @@ $`\begin{align}\quad\quad\quad & = \sum_{n=0}^{+\infty}\dfrac{M^n}{n!} \\
& = \begin{pmatrix} 1 & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 & 1 \\ \end{pmatrix} + & = \begin{pmatrix} 1 & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 & 1 \\ \end{pmatrix} +
\begin{pmatrix} \lambda_1 & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 & \lambda_m \\ \end{pmatrix} + \cdots \\ \begin{pmatrix} \lambda_1 & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 & \lambda_m \\ \end{pmatrix} + \cdots \\
& \\ & \\
& \quad\quad\quad \cdots +\dfrac{1}{2!}\;\begin{pmatrix} \lambda_1 & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 & \lambda_m \\ \end{pmatrix}^2 & \quad\quad \cdots +\dfrac{1}{2!}\;\begin{pmatrix} \lambda_1 & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 & \lambda_m \\ \end{pmatrix}^2
+\cdots \\ +\cdots \\
& \\ & \\
& \quad\quad\quad \cdots + \dfrac{1}{k!}\;\begin{pmatrix} \lambda_1 & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 & \lambda_m \\ \end{pmatrix}^k + \cdots & \quad\quad \cdots + \dfrac{1}{k!}\;\begin{pmatrix} \lambda_1 & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 & \lambda_m \\ \end{pmatrix}^k + \cdots
\end{align}`$ \end{align}`$
......
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