Commit 50f793ca authored by Claude Meny's avatar Claude Meny

Update cheatsheet.fr.md

parent 525239ff
Pipeline #16465 canceled with stage
...@@ -152,9 +152,9 @@ $`\quad\;\; = \;\begin{pmatrix} \displaystyle\sum_{n=0}^{+\infty}\,\dfrac{\lambd ...@@ -152,9 +152,9 @@ $`\quad\;\; = \;\begin{pmatrix} \displaystyle\sum_{n=0}^{+\infty}\,\dfrac{\lambd
<br> <br>
*$`\large{\; M = P\;\begin{pmatrix} \lambda_1 & 0 & 0 \\ 0 & \cdots & 0 \\ 0 & 0 & \lambda_m \\ \end{pmatrix} \;P^{-1}}`$* *$`\large{\; M = P\;\begin{pmatrix} \lambda_1 & 0 & 0 \\ 0 & \cdots & 0 \\ 0 & 0 & \lambda_m \\ \end{pmatrix} \;P^{-1}}`$*
avec les lmbdas valeurs propres et P ... à terminer, en fonction de ce qu'on met avant. <br>
**$`\large\mathbf{e^{\,M}}}`$**$`\;=\displaystyle\sum_{k=0}^{\infty}\dfrac{M^k}{k!}`$ **$`\large{\mathbf{e^{\,M}}}`$**$`\;=\displaystyle\sum_{k=0}^{\infty}\dfrac{M^k}{k!}`$
$`\quad\;=\displaystyle\sum_{k=0}^{\infty}\dfrac{1}{k!}\,P\,\begin{pmatrix}\lambda_1^k & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 & \lambda_n^k\\ \end{pmatrix}\,P^{\,-1}`$ $`\quad\;=\displaystyle\sum_{k=0}^{\infty}\dfrac{1}{k!}\,P\,\begin{pmatrix}\lambda_1^k & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 & \lambda_n^k\\ \end{pmatrix}\,P^{\,-1}`$
...@@ -162,7 +162,7 @@ $`\quad\;=\displaystyle P\left[\,\sum_{k=0}^{\infty}\dfrac{1}{k!}\,\begin{pmatri ...@@ -162,7 +162,7 @@ $`\quad\;=\displaystyle P\left[\,\sum_{k=0}^{\infty}\dfrac{1}{k!}\,\begin{pmatri
$`\quad\;=\displaystyle P\;\begin{pmatrix}\sum_{k=0}^{\infty}\dfrac{1}{k!}\lambda_1^k & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 & \sum_{k=0}^{\infty}\dfrac{1}{k!}\lambda_n^k\\ \end{pmatrix}\;P^{\,-1}`$ $`\quad\;=\displaystyle P\;\begin{pmatrix}\sum_{k=0}^{\infty}\dfrac{1}{k!}\lambda_1^k & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 & \sum_{k=0}^{\infty}\dfrac{1}{k!}\lambda_n^k\\ \end{pmatrix}\;P^{\,-1}`$
**$`\large{\mathbf{e^{\,M}=\displaystyle P\;\begin{pmatrix} e^{\,\lambda_1} & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 &e^{\,\lambda_n}\\ \end{pmatrix}\;P^{\,-1}}}`$** **$`\large{\mathbf{\boldsymbol{e^{\,M}=\displaystyle P\;\begin{pmatrix} e^{\,\lambda_1} & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 &e^{\,\lambda_n}\\ \end{pmatrix}\;P^{\,-1}}}}`$**
...@@ -178,7 +178,7 @@ avec $`I_n`$ matrice carré identité de dimensions $`n\times n`$ ...@@ -178,7 +178,7 @@ avec $`I_n`$ matrice carré identité de dimensions $`n\times n`$
* *$`\large{\mathbf{\big(e^A\big)^{-1} = e^{- A}}}`$* * *$`\large{\mathbf{\big(e^A\big)^{-1} = e^{- A}}}`$*
* *$`\large{\mathbf{e^{\,A}\,A = A\,e^{A\}}} `$* * *$`\large{\mathbf{e^{\,A}\,A = A\,e^{A}}} `$*
* *$`\large{\mathbf{\dfrac{d}{dt}e^{A t} = A\,e^{A t}}}`$* * *$`\large{\mathbf{\dfrac{d}{dt}e^{A t} = A\,e^{A t}}}`$*
......
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