Solution
= Solution
For ordered simple roots, the <Cartan matrix> is $A_{ij}=\langle\alpha_i,\alpha_j^\vee\rangle=2(\alpha_i,\alpha_j)/(\alpha_j,\alpha_j)$. It determines their relative lengths and angles.
= Solution
For ordered simple roots, the <Cartan matrix> is $A_{ij}=\langle\alpha_i,\alpha_j^\vee\rangle=2(\alpha_i,\alpha_j)/(\alpha_j,\alpha_j)$. It determines their relative lengths and angles.