Spectrum of a matrix

The spectrum of a matrix refers to the set of its eigenvalues. If \( A \) is an \( n \times n \) matrix, then the eigenvalues of \( A \) are the scalars \( \lambda \) such that the equation \[ A \mathbf{v} = \lambda \mathbf{v} \] has a non-trivial solution (where \( \mathbf{v} \) is a non-zero vector, known as an eigenvector).