An eigenvalue problem is a matrix equation of the form The problem is to find one (or more than one) non-zero vector \(\vec{x}\), which is called an eigenvector, and the associated \(\lambda \in \math...An eigenvalue problem is a matrix equation of the form The problem is to find one (or more than one) non-zero vector \(\vec{x}\), which is called an eigenvector, and the associated \(\lambda \in \mathbb{C}\), which is called an eigenvalue. Most prominently, they are used to describe the "modes" of a physical system, such as the modes of a classical mechanical oscillator, or the energy states of an atom.
