Linear algebra
StackExchange: Why does every symplectic matrix 𝑀∈Sp(2𝑛,ℝ) admit a symplectic eigenbasis?
Adjoint representation of Lie group
StackExchange: What does the adjoint action of a Lie group on its Lie algebra, Ad:𝐺×𝔤→𝔤, actually give us?
StackExchange: Cartan subalgebra and orbits of the adjoint action
StackExchange: Does semisimple element of a semisimple complex Lie algebra belong to some Cartan subalgebra?
StackExchange: Diagonalizing elements of compact lie groups
Cartan subalgebra
StackExchange: How does one proceed in finding a Cartan subalgebra?