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packages/macros.sty : Added convinences macros

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saundersp
2024-11-07 05:29:13 +01:00
parent 94cdd07e84
commit aafcec6a3e
5 changed files with 46 additions and 36 deletions
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8
contents/algebra.tex
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@ -56,11 +56,11 @@ Un matrice est une structure qui permet de regrouper plusieurs éléments d'un c
\subsection{Trace}
%TODO Complete subsection
$\forall A \in \mathcal{M}_{n}, tr(A)=\sum_{k=0}^na_{kk}$
$\forall A \in \mathcal{M}_{n}, tr(A)=\sum\limits_{k=0}^na_{kk}$
$tr\in\mathcal{L}(\mathcal{M}_n(\K),\K)$
$\forall(A,B)\in\mathcal{M}_{n,p}(\K)\times\mathcal{M}_{p,n}(\K), tr(AB) = tr(BA)$
$\forall(A,B)\in\mathcal{M}_{n,p}(\K)\cartesianProduct\mathcal{M}_{p,n}(\K), tr(AB) = tr(BA)$
\langsubsection{Valeurs propres}{Eigenvalues}
%TODO Complete subsection
@ -80,12 +80,12 @@ $Eigenvalues = m \pm \sqrt{m^2-det(A)}$
\langsubsection{Déterminant}{Determinant}
%%TODO Complete subsection
$\function{D}{\mathcal{M}_{m\times n}(\R)}{R}$
$\function{D}{\mathcal{M}_{m\cartesianProduct n}(\R)}{R}$
\langsubsubsection{Axiomes}{Axioms}
%%TODO Complete subsubsection
$\forall M \in \mathcal{M}_{m\times n}$
$\forall M \in \mathcal{M}_{m\cartesianProduct n}$
\begin{itemize}
\item{$\forall \lambda \in \K, D(\lambda M) = \lambda D(M)$}
\end{itemize}