Lie groups and Lie algebras: Dual Killing form and semisimplicity

We discuss nondegeneracy of the Killing form and see (in some gory detail) how this allows us to equip our weight diagrams with a Euclidean geometry provided we're working with a compact semisimple group. A fair bit of this video is just linear algebra about duals of nondegenerate forms, which can be skipped if you know it (but I wanted to assume minimal prerequisites).