orthogonal eigenvectors?

Question

I have a very simple question that can be stated without proof. Are all eigenvectors, of any matrix, always orthogonal? I am trying to understand Principal components and it is cruucial for me to see the basis of eigenvectors.

Answer 1

The answer is no. But this does not contradict the fact that they can form a basis. A basis is a set of linearly independent vectors that spans the space under consideration. They don’t have to be orthogonal to one another.