Let M {\displaystyle {}M} be a real n × n {\displaystyle {}n\times n} -matrix. Let a ∈ R {\displaystyle {}a\in \mathbb {R} } be a real number, and suppose that it is an eigenvalue of M {\displaystyle {}M} , considered as a complex matrix. Show that a {\displaystyle {}a} is already over R {\displaystyle {}\mathbb {R} } an eigenvalue of M {\displaystyle {}M} .
