structural:summarization
Additional properties of eigenvalues

Let A {\displaystyle A} be an arbitrary n × n {\displaystyle n\times n} matrix of complex numbers with eigenvalues λ 1, …, λ n {\displaystyle \lambda _{1},\ldots,\lambda _{n}}. Each eigenvalue appears μ A (λ i) {\displaystyle \mu _{A}(\lambda _{i})} times in this list, where μ A (λ i) {\displaystyle \mu _{A}(\lambda _{i})} is the eigenvalue's algebraic multiplicity. The following are properties of this matrix and its eigenvalues: