---- > [!definition] Definition. ([[cartan matrix]]) > Let $(\Phi, E)$ be a [[root system]] with [[root basis]] $\Delta=\{ \alpha_{1},\dots,\alpha_{\ell} \}$. [[reflection|The integers]] $\langle \alpha_{i}, \alpha_{j}^{\vee} \rangle$ are called **cartan integers**, and the $\ell \times \ell$ matrix $C=(\langle \alpha_{i}, \alpha_{j}^{\vee} \rangle)_{1 \leq i,j \leq \ell}$ is called the **cartan matrix**. > > Cartan matrices may be represented as [[Dynkin diagram|Dynkin diagrams]]. ^definition ---- #### ---- #### References > [!backlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM [[]] > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ``` > [!frontlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM outgoing([[]]) > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ```