Principle axis theorem, leads on from perron’s theorem. Since a proof of perron’s theorem I read for symmetric positive matrices, uses the principle axis theorem to show that it has a positive eigenvalue.
Every symmetric matrix is diagonalizable.
Essentially as far as I can tell, the spectral theorem says this. According the my resource this is often called the principle axis theorem.
Anyway the proof the PAT use the ST, and is rather short. They are rather related it seems.
Princple axis theorem for quadratic forms, shows given a quadratic function, you can find a basis which is the principle axis of the quadratic. Damn text and it’s math limitations!