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Definition D5862
Complex matrix eigenvalue

Let $A \in \mathbb{C}^{N \times N}$ be a D6159: Complex square matrix.
A D1207: Complex number $\lambda \in \mathbb{C}$ is an eigenvalue for $A$ if and only if $$\exists \, z \in \mathbb{C}^{N \times 1} \setminus \{ \boldsymbol{0} \} : A z = \lambda z$$
Children
 ▶ Complex matrix eigenvalue sequence ▶ Complex matrix singular value ▶ Real matrix complex eigenvalue
Results
 ▶ Characterisation of complex matrix eigenvalues in terms of characteristic polynomial ▶ Squared eigenvalue is an eigenvalue for the square of a complex matrix