Commit f018fe57 authored by Claude Meny's avatar Claude Meny

Update cheatsheet.fr.md

parent d2abd139
Pipeline #16459 canceled with stage
...@@ -67,7 +67,7 @@ $`= \begin{pmatrix} \lambda_1 & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 & \lambda_m\\ \ ...@@ -67,7 +67,7 @@ $`= \begin{pmatrix} \lambda_1 & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 & \lambda_m\\ \
Et par récurrence, Et par récurrence,
$`\forall k \in \mathbb{N}^{*}\{1}`$ <!--\setminus --> $`\forall k \in \mathbb{N}^{*}\setminus\{1\}`$ <!--\setminus -->
**$`\mathbf{M^k}`$** $`\; = M^{k-1}\times M`$ **$`\mathbf{M^k}`$** $`\; = M^{k-1}\times M`$
...@@ -78,11 +78,9 @@ $`\quad = \begin{pmatrix} \lambda_1^{k-1} & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 & \ ...@@ -78,11 +78,9 @@ $`\quad = \begin{pmatrix} \lambda_1^{k-1} & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 & \
##### $`M`$ est non diagonale, mais diagonalisable`$ ##### $`M`$ est non diagonale, mais diagonalisable`$
<br>
*$`\mathbf{M^2}`$* $`\; = M\times M`$ *$`\mathbf{M^2}`$* $`\; = M\times M`$
$`\quad = P\,\begin{pmatrix} \lambda_1 & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 & \lambda_m\\ \end{pmatrix}\,\underbrace{P^{-1}\;\times\; $`= P\,\begin{pmatrix} \lambda_1 & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 & \lambda_m\\ \end{pmatrix}\,\underbrace{P^{-1}\;\times\;
\; P}_{\color{blue}{= I_m}}\,\begin{pmatrix} \lambda_1 & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 & \lambda_m\\ \end{pmatrix}\,P^{-1}`$ \; P}_{\color{blue}{= I_m}}\,\begin{pmatrix} \lambda_1 & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 & \lambda_m\\ \end{pmatrix}\,P^{-1}`$
$`= P\,\begin{pmatrix} \lambda_1 & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 & \lambda_m \\ \end{pmatrix}^{\,2}`$ $`= P\,\begin{pmatrix} \lambda_1 & 0 & 0 \\ 0 & \ddots & 0 \\ 0 & 0 & \lambda_m \\ \end{pmatrix}^{\,2}`$
......
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