Given a square matrix \( {\rm A} \in \mathbb{C}^{{n \times n}} \), the eigenvalue problem consists in finding a scalar λ (real or complex) and a nonnull vector x such that $${\rm Ax} = \lambda{\rm x}$$ (6.1) Any such λ is called an eigenvalue of A, while x is the associated eigenvector. The latter is not unique; indeed all its multiples αx with α≠ 0, real or complex, are also eigenvectors associated with λ. Should x be known, λ can be recovered by using the Rayleigh quotient \( {\rm x}^H {\rm Ax/}\left\| {\rm X} \right\|^2, {\rm x}^H = {\rm \bar{x}}^{\rm T} \) being the vector whose i-th component is equal to \( \bar{x}_{i} \).