Let A∈CN×N be a D6159: Complex square matrix.
A D1207: Complex number λ∈C is an eigenvalue for A if and only if
\begin{equation}
\exists \, z \in \mathbb{C}^{N \times 1} \setminus \{ \boldsymbol{0} \} :
A z = \lambda z
\end{equation}
Children
| ▶ | D6192: Complex matrix eigenvalue sequence |
| ▶ | D6226: Complex matrix singular value |
| ▶ | D5976: Real matrix complex eigenvalue |
Results
| ▶ | R5079: Characterisation of complex matrix eigenvalues in terms of characteristic polynomial |
| ▶ | R5556: Squared eigenvalue is an eigenvalue for the square of a complex matrix |